Here is the full list of all 42 Monolith achievements.
Won the game on Sudden Death Lethality
Get an S Rank in Time (Under 20 minutes).
Get all 4 S Ranks in one run.
Tarnish notte the majesty! (Acquired all Hats)
Get an S Rank in Damage (10 hits or fewer)
Won the game on Intense Lethality.
Won without getting any upgrades.
Won without getting any weapons.
Get an S Rank in Secrets (Find all secrets)
Finished a run with a score of 100,000.
This is what you wanted, isn't it?
Pass the seal. (Floor 6)
Leave that poor cat alone.
Get an S Rank in Exploration (Visit all rooms)
Reach the Temple.
Defeated the Overlord.
Reach the Sanctum (Floor 5).
Reach the Bellows (Floor 4).
Reach the Maintenance System (Floor 3).
Reach the Archives (Floor 2).
Reach the Excavation (Floor 1).
Become the reigning tag champion.
Finished a run with a score of 200,000.
Protect Blastcore's smile.
Reach a highscore of 20 minigames in the Hub.
Take a screenshot containing 100 bullets.
Admire a fine portrait.
Finished a run with a score of 300,000.