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