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