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