Here is the full list of all 34 Fist's Elimination Tower achievements.
Clear 13 floors without getting eliminated
Clear an entire leg without getting eliminated
Clear 77 floors without getting eliminated
Clear 150 floors without getting eliminated
Hop on 100 Mun-muns
Hop on 777 Mun-muns
Hop on 3333 Mun-muns
Hop on 12 Mun-muns that explode into bees
Reach the Pinky Room
Reach the Ring Room
Reach the Middle Room
Reach the Index Room
Reach the top of the tower
Win $7,000 Overall
Win $25,000 Overall
Win $100,000 Overall
Win all accessories and expansions available from the spin board
Win more than $5,000 during one run of the tower
Admire the differences between the two cat accessories
Lean against a wall for a total of 10 seconds as a horse
Clear 3 floors as That Slow Crab
Create a contestant
Defend the left side of the menu screen for 90 seconds
Beat the Right-Hand Tower
Beat the Right-Hand Tower on Iron Fist mode
Beat the Right-Hand Tower on Allison Fist mode
Beat the Southpaw Tower
Beat the Southpaw Tower on Iron Fist mode
Beat the Southpaw Tower on Allison Fist mode
Beat the Right-Hand Tower in under 9 minutes
Beat the Right-Hand Tower in under 8 minutes
Beat the Southpaw Tower in under 10 minutes
Beat the Southpaw Tower in under 9 minutes
Unlock all of the other achievements