Here is the full list of all 37 Jet Gunner achievements.
Complete the first stage
Complete the second stage.
Complete the third stage
Complete the forth stage
Complete the fifth stage
Complete the final stage
Complete challenge 1-1
Complete challenge 1-2
Complete challenge 1-3
Complete challenge 1-4
Complete challenge 1-5
Complete challenge 2-1
Complete challenge 2-2
Complete challenge 2-3
Complete challenge 2-4
Complete challenge 2-5
Complete challenge 3-1
Complete challenge 3-2
Complete challenge 3-3
Complete challenge 3-4
Complete challenge 3-5
Complete challenge 4-1
Complete challenge 4-2
Complete challenge 4-3
Complete challenge 4-4
Complete challenge 4-5
Complete challenge 5-1
Complete challenge 5-2
Complete challenge 5-3
Complete challenge 5-4
Complete challenge 5-5
Complete stage 1 under HARDCORE mode
Complete stage 2 under HARDCORE mode
Complete stage 3 under HARDCORE mode
Complete stage 4 under HARDCORE mode
Complete stage 5 under HARDCORE mode
Complete the game under HARDCORE mode