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