Here is the full list of all 24 Blasting Agent: Ultimate Edition achievements.
Clear Level 6 on Normal Difficulty
Unlock the Pule Bazooka Upgrade
Clear Level 5 on Normal Difficulty
Unlock the Repulsor Shield Upgrade
Clear Level 4 on Normal Difficulty
Unlock the Grav Jump Ability
Clear Level 3 on Normal Difficulty
Unlock the Frag Grenade Upgrade
Clear Level 2 on Normal Difficulty
Unlock the Spiked Boots Upgrade
Clear Level 1 on Normal Difficulty
Unlock the Ionic Dash Ability
Unlock the Yeti Costume
Unlock the Ninja Costume
Unlock the Bearded Brother Costume
Unlock the Space Captain Costume
Unlock the Batty Guy Costume
Unlock the Polychromatic Suit Costume
Clear Level 1 on Hard Difficulty
Clear Level 2 on Hard Difficulty
Clear Level 3 on Hard Difficulty
Clear Level 4 on Hard Difficulty
Clear Level 5 on Hard Difficulty
Clear Level 6 on Hard Difficulty