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