The rule concerning cores is that if you kill a Robot (not mechas) with a super-effective move, you have a 50% of getting their core from them. For example, If you finished Fire Man off with an Ice Slasher, you'd have a 50% of getting his Flame Core from him.
What this means is that if no robots in the game have, say, a Laser Core, then you can't get a Laser Core as of now. From your list, you CAN get a:
Crystal Core from Gemini Man, Jewel Man, or Crystal Man Copy Core from Mega Man, Bass, Proto Man Neutral Core from Disco, Rhythm, Roll, Enker, Punk, or Ballade. I may have missed some robots... Happy hunting!
Neutral: Roll, Rhythm, Disco, Enker, Punk, or Ballade. (Quint not included. lol) Copy: Mega Man, Proto Man, or Bass. Shield: Wait for King or Shield Man to be released, then go to them. Laser: You'll have to fire your lazor for the core when Laser Man or Terra is around. Crystal: Gemini Man, Crystal Man, and Jewel Man. Space: Star Man. (And Ring Man, apparently. Unless Mikey/Mike is wrong, but idk)
You're welcome. I think I should make a core hunt guide...
...Ring Man only drops Cutter Cores. Only Star Man can drop Space Cores at this point. Think about it, robots ALWAYS drop Cores that match their actual element. Ring Man is a Cutter-type robot that happens to be in a Space-themed stage.