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