Here is the full list of all 42 Monolith achievements.
Admire a fine portrait.
Finished a run with a score of 200,000.
Get an S Rank in Damage (10 hits or fewer)
Protect Blastcore's smile.
Become the reigning tag champion.
Won without getting any weapons.
Won the game on Intense Lethality.
Get an S Rank in Secrets (Find all secrets)
Get an S Rank in Time (Under 20 minutes).
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)
Tarnish notte the majesty! (Acquired all Hats)
Reach the Temple.
Leave that poor cat alone.
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).
Get all 4 S Ranks in one run.
Won without getting any upgrades.
Won the game on Sudden Death Lethality
Reach a highscore of 20 minigames in the Hub.
Take a screenshot containing 100 bullets.
Finished a run with a score of 300,000.