I never played vanguard in SP, but based on my MP experience, take Reave as bonus power(or you can take Kaidan as Team mate). Level up your Charge, Nova, and Incendiary Ammo. The other powers are far less important

Charge: Rank 4 - Force & Damage, Rank 5 - Power Synergy, Rank 6 - Barrier
Nova: Rank 4 - Radius, Rank 5 - Power Recharge*, Rank 6 - Pierce Sustain
Incendiary Ammo: Rank 6 - Explosive Burst(the rest of the rank are far less important, so spec as you like)
Reave: Rank 4 - Radius, Rank 5 - Recharge Speed, Rank 6 - Damage and Duration
Fitness: just improve your shields.
Assault Mastery: go for power damage

Weapons -  Preferable a light weight weapons to get your cooldown to be 200%

here is the tactic,

1) equip your gun with Incendiary Ammo,
1.5) use Nova(yes, with no enemies around you, use your own discretion whether you want to skip this step)
2) Cast Reave on a group of enemies(as your shield begins to recover from Nova)
2.5) use Nova again (these .5 steps can be skipped if you do not follow my build on Rank 5 Nova)
3) Charge an Enemy that got Reaved
4) before the Charge hit the enemy, press R1 and hold it,
5) when the charge hit, the gun will be fired at that same moment so
6) the charge will cause a biotic explosion, and the fired shot with Incendiary Ammo will have 50% chance of causing an AoE Fire Burst as well, then
7) if that double explosion did not kill all the enemies around you, follow up with a Nova, so
8) there should still be active Reave effect in other enemies in the area so, the Nova will cause another Biotic Explosion, combined with the damage of Nova, the only enemies that should still be alive after this are either Banshees or Atlas, which you should not be charging into if you see them. (should it ever comes to this, charge them to restore your shield and get away)
Reave -> Charge -> Nova is a proven tactic in MP. I added Incendiary Ammo when I thought of SP build, you may have to feedback on me on how well that works.

*there is some debate on Nova Rank 5. the option is half blast or power recharge. you have more survivability with half blast. but Power Recharge effect(Increase recharge speed of all powers by 25% for 15s)stacks, so if you use Nova when there is no enemies around whenever you can(use it once you see your shield auto recharging, which normally takes 3-5 seconds), you can stack up and maintain a 75% bonus to cooldowns at any time. that and couple with 200% cooldown bonus from weapons, your Charge cooldown is less than 1 second. But you may not like the idea if you don't like these glass cannon strategy.