1) Your squad sidequest is basically there for you to help them takes their minds of from their personal problems so that they may concentrate on the mission.

2) Getting the right person to lead certain groups in the last mission is also crucial, you can check whose the right person for the job by reading their profile in the character select screen.

I decided to create a guide kind of geared toward players who have tried the class, but wanted to give the Vanguard another try on one of the harder difficulties. A lot of credit goes to some of the community who have shown that Vanguards are not only a viable option, but a "Charge focused" Vanguard can be a powerhouse even on Insanity. Also, kudos to Sinosleep for posting a few vids of him running through Insanity and putting Vanguard back on the map for any unbelievers. Also, this guide still holds merit for the Veteran and below difficulty levels, however, due to the lack of defense on most enemies (defense being armor/shields/barrier), you'll find you can ignore some parts and have a little more wiggle-room with the Squad Points and what-not.

I should really preface the below info by saying that the road to High Risk, High Reward is paved with the Replay button... at first. Before you get the hang of how Charge can work for and against you it can be tough, but once you get the hang of it, the Vanguard goes from being frustrating to a powerful and extremely exciting class. It really is geared for people who want to be in the midst of the action constantly.

I'll start with my take on equipment and my build and then go on to different situations, strategies, and tactics. Remember, this is what works for me. Experienced players can and will be able to use any number of variations to the above.

First off, the three shotguns: My own experience is that the Calymore is definitely the highest risk, highest reward weapon for the Vanguard. Less ammo, reload after every shot, but tons of damage. The Assault shotgun has much less damage but lets you fire off several rounds rapidly, which was great for me when I first started playing and hadn't maxed out the Charge ability. The Katana (starting shotgun) is a happy medium between the two.

Equipment: You'll probably want to get the arms that give you 10% more Thermal Clips as soon as you can. Before you get the shotgun upgrade that doubles your Thermal Clip capacity, and especially with the shotgun in general, every extra round you can fire off is extremely important.

Kudos to Sinosleep for this next one: Get the headgear that does 10% extra headshot damage. With Heavy Charge you should have enough time to line up your shotgun for a headshot and a one shot kill 80-90% of the time.

Get the shoulder armor that increases melee. 25% is a big number. Add that to the research upgrade for Shep's melee damage for a vicious shotgun-melee combination.

The rest is really up to you. The health and shield upgrades may be good, but I haven't seen a significant difference in survivability to merit any true concern. I will say that for those that have the Dr. Pepper DLC, the Recon Hood is a decent replacement if you find that lining up headshots is not working out so well.

The Build: Ok, so this is the most debateable part of the post...
Here's my rundown on how to allocate your points for an agressive Vanguard build.
Incendiary Ammo: 2
Cryo Ammo: 4 (Squad Cryo)
Charge: 4 (Heavy Charge)
Vanguard: 4 (forget the name, go with the one that gives the best cooldown bonus. I think it's Bastion)
AP Ammo: 4 (Tungsten Rounds)
Put the rest wherever you want them. I used the points for Shockwave, which I'll explain later.

From top to bottom:
I got level 2 Incediary Ammo just to unlock Cryo. Squad Cryo Ammo is great. You can turn it on, then switch to AP Ammo and your squad actually keeps the Cryo Ammo on. You'd be surprised how often you'll run across frozen enemies just waiting to be shattered, even on Hardcore/Insanity. By surprized at how much, I really do mean several enemies during each encounter.

I went for Heavy Charge simply for the slow-mo action. Gives you plenty of time to line up your shot. Area Charge would be better suited for Veteran and below where most enemies do not have Shields or Armor.
Your passive Vanguard skill: You want the extra cooldown. Charge is such a big part of your strategy and with its 100% shield recovery, you want it up ASAP.

AP Ammo: This is where a lot of people will say Reave, but I stick with AP Ammo. Not only is it a passive skill that you turn on and forget about, but it gives you 70% more damage to armor and health, and armor is the Vanguard's only weakness. Shotguns do great against health, shields, and barriers, but are weak against armor. The Tungsten rounds (and Claymore) finally give you a fighting chance. Now, why AP and not Incendiary? Incendiary Rounds do damage over 3 (or 4, not sure which) seconds, AP Ammo damage is immediate. It's important for the Vanguard to do high burst damage, which is why your shotgun, ammo, and playstyle should be tailored to getting as close to "1 shot, 1 kill" as possible. AP Ammo helps. I will say that on Veteran and below, Incendiary is a better choice since you won't be running into that much armor, and you really don't need a bonus power, though it's always nice. Just don't take an anti-shield power. You'll learn later, shields work for you.
From there, really, you can do what you want. Pull or Shockwave. I went with Shockwave because it works well vs. frozen enemies or getting enemies to pop out of cover so you can target them with Charge (even with shields or armor, they will stagger).

Strategy:
My main focus with my Vanguard was to always be on the offense. Charge is your bread and butter power, but all your damage should come from your shotgun with melee to clean up. Also, with Heavy Charge, your optimum target will still have some sort of defense, be it shields, barrier, OR armor (not shields/barrier AND armor). Sounds crazy, I know, but hear me out. A shielded enemy will stagger while you line up the shot for a kill as opposed to a defenseless enemy which will be go flying, causing you to have to either chase them down, or be a crack shot (which I'm really not). If you don't, they will be back to haunt you. Thankfully, with a few upgrades (and especially with the Calymore), shields will be worthless to them as you will shoot right through. The Claymore can 1 shot kill an enemy with full shields and health. Add Tungsten Rounds and the same goes for armor. You'll need a bit of help with enemies who have armor and shields/barrier, but that's what squadmates are for.

Who to Charge? Charge for me is all about positioning. Aside from the shelds/armor rule, you need to go for the guy who is where you want to be. A guy who jumps over low cover is a great target. Charge, kill, and take cover. If there are enemies on the other side, even better. Pop up and kill, drop back into cover. Don't Charge them. Getting flanked? Stay where you are, get your squadmates to soften them up and shoot them as they come around the corner, then look for your next target. The first Charge is so important because it puts you in your "home" position without having to run through all that oncoming fire (which on Hardcore/Insanity will drop your shields and health fast!). Try to keep your Squadmates constantly focused "two Charges ahead of you." Lastly, if you see a non-boss target alone behind the rest of the group, Charge. Enemies will turn to face you and your Squadmates will be free and clear to clean them up. Just remember, keep moving forward, your ammo supply depends on it.
Vs. Collectors: Squadmates should be focused on the Collector General while you mop up all other Collectors. You don't want to have to kill him 3-4 times in one encounter. It gets easier and easier to Charge, shoot, move on to the next... Charge, shoot, do it again.

Vs. Husks: Squad Cryo Ammo and Grunt/Zaeed/Jacob to take the heat and freeze as many as possible while you clean up.

Vs. Scions: Once you get the pattern down you can wait for them to send a Shockwave, Charge past it, shoot, back up, wait for Shockwave, Charge past it, rinse, repeat. Don't forget to use your Squadmate's powers when available.

Vs. Geth: Your standard Geth are pretty easy since they will only have shields and pitiful health. Bring Miranda and Garrus with you for earlier missions to whittle down the tougher ones while you focus on the regular troopers. Geth generally are all shields which the shotgun chews through. During the Colossus fight, you will want to have the Tempest handy as it's not necessarily the brightest idea to go charging around in the sun with little cover and a Colossus raining heavy artillery at you.

Vs. Krogan/Vorcha: Honestly, these guys are tough at first since you have little to no upgrades and they all have armor, but later in the game they become easier. Switch to your Handcannon to hit the flame tanks on the appropriate Vorcha to take out a few enemies. Have your Squadmates use their Handcannons as well with Cryo ammo turned on. Their armor will drop fast and you'll be Charging whole groups of frozen enemies (or Shockwave them if they are grouped close). Multiple Krogan work for you since you can Charge back and forth out of range from their shotguns and right through their Krogan charge. Also of note: there always seems to be explosive crates or containers around with these guys, so blow them up at a distance before closing in.

Vs. Mechs: Let the dog Mechs close in or have your squadmates take them as they approach since they will never be in cover. Usually dead before they reach you (Varren too). Loki Mechs are easy 1 shot 1 kill, just be careful because if you get a clean headshot or if they are frozen but not dead, they tend to explode. That sucks. Take the YMIR Mechs from cover. Sometimes you just don't Charge in.

Vs. Mercs: This includes the Eclipse and Blue Suns (the Humanoid enemies). Stick to the Shield and positioning rules. Have your Squadmates focus on anyone with multiple defenses. Avoid positions where they can hit you with rockets from multiple angles. My main problem with these guys is getting cocky, which usually ends up with me dying gloriously. I do think a good fight is one where I'm in the red for most of it. Really gets the adrenaline going. These guys tend to stay together and in cover more than anyone else to beware of Charging into the middle of groups of 3 or more. If they don't seperate, I've Charged right in, taken one out and hopped right back over their cover with barely any Health left but still somehow alive. Don't necessarily try that at home.

A few tips:
Anytime you hear Shepard say, "I can't target them!" It means you are about to die.

If you are using the Claymore, you need to be aware of whether or not you've reloaded. I don't know how many times I've Charged before reloading and it sucks. Luckily, you've just regained your shields... whoops, you're playing on Hardcore/Insanity, you've just lost them again.

When in doubt, bring Miranda. With Overload, Warp, and Cerberus Officer for squad bonuses, she's "a great addition to the team," as Jacob would say. Throw in the Tempest for more fun.

On the Collector Ship: You can't Charge from platform to platform. You'll stop right at the edge. You really need to play this agressive - high risk, high reward - and get up on that platform before you Charge. At least you've now received the Claymore and all your problems are over.... or just beginning.

Zaeed and Grunt with Squad Cryo Ammo makes Grunt's Loyalty mission a cakewalk. Technically you can take Garrus instead of Zaeed, but the point is to have Grunt with Assault Rifle, Zaeed with the Mantis Sniper. With that combo, the only thing I did was run around cleaning up a few left over frozen enemies. Bring the Cain to take a good chunk out of the Thresher Maw's armor, and finish with your heavy pistol. The Krogans at the end are pretty basic. I don't think I even needed cover for that fight. Charge, Melee, Charge, Melee.

Anytime you know you will face husks, bring Grunt. Put him right in the middle of the action and just watch his back. IFF mission comes to mind. I think that was another Grunt/Zaeed mission for me.
Double Scions can be trouble. If you can get their Shockwaves in sync, you can use the regular strategy above. If not, well, it sucks no matter what build you are. Cain.

Speaking of which: Any mission with a Praetorian, bring the Cain and use it on him/it, then do your best with the rest of his armor. Hope that the blast got rid of any lingering Collectors/Husks that he brought with him.

Try to tailor your mission order to maximize your Shotgun and Biotic Recharge bonuses as early as possible.

Final Thoughts:
I can't stress enough on learning where/who to Charge. Also, as easy as it is to get in there and start Charging all over the place, you'll find life much easier (and lasting longer) when you are aware of your surroundings (where safe cover is, where the enemies are). So get out there and have fun. If you took one thing away from this long post, then I think it was a success. Thanks for reading.