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