Rare cores are easy, just follow main storyline until chapter 8 *spoiler alert*
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Stop at World Tree level 2, don't goto 7th level/perimeter else too late already
then stop story line and start farming/grinding everything else. You can get Legendary Core from some level 60+ unique monsters easily. I always farm soul eater stanley.
LOL, I've burn 2x-3x your cores recently, did not get any rare, I'm still like 5-7 rares missing.
10+ legendaries, 100+ rare, 200+ commons, 150+ boosters
I'm done with maxing quite a few rares like Zenobia, Mythra (S7), Praxis, Aegeon, Roc, Godfrey, Agate, Ursula, Dagas, Boreas, Herald, Sheba (gold digger), and already open up level 5 affinity for like half of the rares.
Zenobia is fun, to search and fight the UM one by one.
Some really time grinding stuff are Ursula, Dagas, Vess, a few b!tch3s to prepare for the Girl Power Off

(i'm still looking for Vale), spent a lot of money (like 2M+ coins so far) but sell to earn a lot (like 5M+ so far)
The rest are just normal grinding, I'll be upgrading Kassandra, Perun, Theory, and a few more.
240+ hours into grinding ... 2M+ coins excluding 25 legendary and 99 gold cylinders.
That's a long, long grind. Excluding story mode, now got around 6 more "bad ass looking blades" to grab. Now time out, grind the trust and affinity quests dulu, since got a few edi. Should be good for lots of hours.