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