General

you have to buy a core from the evo shop, then do an incredibly easy quest. after you do that, your slots will expand to 6

Ahh, thank you. What about unlocking the other core slots? Do I have to do the quests inside?

There's a core called something amongst the lines of "Drop of 120 Necromancer Weapons". You can't buy it, you get it from core drops. Just evo for a bit and you'll get that core eventually~

You get the core from the monsters inside Evo Lab and then use it. .3.'