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