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