Here is the full list of all 31 TOKOYO: The Tower of Perpetuity achievements.
Climb 25 floors
Achieve 5 bonus score chains
Reach the Light Danger Area
Reach the Danger Area
Climb 50 floors
Climb 100 floors
Climb 250 floors
Get hugged by a Succubus 5 times
Get hugged by a Maid Succubus 5 times
Get your blood sucked by a Vampire 5 times
Reach the Absolute Danger Area
Reach the Hopeless Area
Reach the Unknown Hopeless Area
Reach maximum karma
Collect 10 log pieces
Collect 25 log pieces
Collect 50 log pieces
Collect 101 log pieces
View the ending with Cocoa
View ending with Shippo
View ending with Kanae
View ending with Kukuri
View ending with Imibi
Defeat the Demon Queen Erloa
Defeat the Immortal Nanaha
Defeat Lula of the Dark Star
Defeat Riim the Irreversible End
Achieve 10 bonus score chains
Achieve 20 bonus score chains
Reach the summit two days in a row
Reach the summit three days in a row