Here is the full list of all 12 Cobalt Core achievements.
Unlock the Gemini.
Unlock the Jupiter.
Unlock Books.
Unlock Max.
Unlock Drake.
Unlock Isaac.
Unlock CAT.
Unlock the Ares.
Unlock the Tiderunner.
Win a run on the hardest difficulty.
Beat the finale.
Win a fight you shouldn't have started.