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