Here is the full list of all 22 The Monster Within achievements.
Unlock a card pack
Take three afflictions in one run
Win 10 runs
Win 50 runs
Deal 100 damage in one turn
Unlock all afflictions
Unlock all card packs
Unlock all monsters
Win a run as the Blob
Beat blood level 0
Beat blood level 1
Beat blood level 3
Draw 20 cards in a turn
Play every card in your deck in one turn
Take an extra turn
Beat all level 3 bosses
Win a run as the scientist
Summon a god
Win a run as the Parasite
Win a run as the Plant
Win a run as Vampire
Win a run as Wraith