Here is the full list of all 19 IWO: Bloodbath in the Bonins achievements.
Reach the conclusion of an invasion
Attain a US defeat
Capture Mount Suribachi
Defeat 40 Japanese Defenders
Transfer all reserves in one game
Defeat 20 Japanese Defenders
Start a new game
Attain a draw
Attain a US victory
Attain 2 US victories
Attain 3 US victories
Defeat 70 Japanese Defenders
Defeat 110 Japanese Defenders
Land on both beaches
Capture 2 Sectors (excluding Mount Suribachi)
Complete a game without transferring any reserve units
View the Credits Screen
Research Iwo Jima
Learn the game's rules