Here is the full list of all 22 The Monster Within achievements.
Beat blood level 0
Win a run as Vampire
Take three afflictions in one run
Unlock a card pack
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 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 Wraith