Here is the full list of all 97 Vertical Strike Endless Challenge achievements.
Shot down 10 enemies with semi-active missiles
Shot down 100 enemy air units in total
Defeated 50 total waves in Anti-Aircraft and Anti-Ship combat
Survived 15 minutes in Anti-Ship combat
Defeated Wave 15 in Anti-Ship combat
Sunk 50 total ships
Defeated 20 total waves in Anti-Ship combat
Defeated 10 waves in Anti-Ship combat within 15 minutes
Defeated Wave 10 in Anti-Ship combat
Defeated 15 total waves in Anti-Ship combat
Sunk 20 total ships
Recover from stall at less than 200 meters high
Defeated 30 total waves in Anti-Aircraft and Anti-Ship combat
Used all missile-type sub-weapons at least once. (Lock-on required)
Obtained results from using all types of sub-weapons
Used special armament: ATM-65
Used all type of bombs at least once
Used special armament: DWS-49
Defeated Wave 15 in Anti-Aircraft combat
Defeated 20 total waves in Anti-Aircraft combat
Shot down 50 enemy air units with missiles
Shot down 50 enemy air units in total
Defeated Wave 10 in Anti-Aircraft combat
Defeated 10 waves in Anti-Aircraft combat within 15 minutes
Defeated 15 total waves in Anti-Aircraft combat
Defeated Wave 5 in Anti-Aircraft combat
Defeated 5 waves in Anti-Aircraft combat within 5 minutes
Shot down 20 enemy air units in total
Took flight with only missile-related subweapons
Shot down 15 enemy air units in total
Shot down 10 enemy air units in 1 sortie
Used special armament: AAM-9
Used all type of missiles assigned to Fox 2 call
Shot down 5 enemy air units in 1 sortie
Used special armament: BK-372
Shoot down an enemy air unit with Fox 1
Shoot down 3 enemy air units within 1 minute
Used all type of machine-guns at least once
Defeated Wave 1 in Anti-Aircraft combat
Used special armament: Rb. 163
Shoot down an enemy air unit with Fox 3
Used all type of missiles assigned to Fox 1 call
Used special armament: AAM-120
Used all type of missiles assigned to Fox 3 call
Engage Endless Mode (Anti-Aircraft)
Cut the limiter total 152 second
Sunk 15 total ships
Used special armament: ARM-88
Fired 3 machine-guns simultaneously.
Used special armament: GAU-22
Defeated Wave 5 in Anti-Ship combat
Defeated 5 waves in Anti-Ship combat within 5 minutes
Equip weapons to all weapons bays and use all at least once
Used all rocket-type sub-weapons at least once.
Used special armament: ARA-72
Shoot down an enemy air unit with Fox 2
Used special armament: MK. 181
Sunk 2 ships within 3 minutes
Defeated Wave 1 in Anti-Ship combat
Used special armament: NM-44
Disabled angle of attack limiter.
Used special armament: ASM-2
Flew faster than Mach 1
Engage Endless Mode (Anti-Ship)
Flew while using manual flares
Flight time exceeds 1 hour
Defeated Wave 20 in Anti-Aircraft combat
Defeated Wave 20 in Anti-Ship combat
Survived 15 minutes in Anti-Aircraft combat
Survived 30 minutes in Anti-Aircraft combat
Survived 30 minutes in Anti-Ship combat
Fired a fixed machine-gun until it was empty
Fly over 10,000 meters for the first time
Flew above Mach 2 for more than 10 seconds
Shot down 150 enemy air units in total
Shot down 200 enemy air units in total
Defeated 50 total waves in Anti-Aircraft combat
Defeated 100 total waves in Anti-Aircraft combat
Defeated 50 total waves in Anti-Ship combat
Defeated 100 total waves in Anti-Ship combat
Survived more than 45 minutes in Anti-Aircraft combat
Survived more than 45 cumulative minutes in Anti-Ship combat
Survived more than 60 minutes in Anti-Aircraft combat
Survived more than 60 cumulative minutes in Anti-Ship combat
Defeated 128 total waves in Anti-Aircraft and Anti-Ship combat
Survived more than 120 minutes in Anti-Aircraft and/or Anti-Ship combat
Took flight without a sub-weapon equipped
Took flight with only gunner-type subweapons
Took flight with only bomb-type subweapons
Took flight with only rocket-related subweapons
Took flight with only rocket, gunner, and bomb-type subweapons
Fling off a missile while disabling the AoA limiter
Sunk 100 total ships
Congratulations! Obtained all other achievements!
Shot down 50 enemy air units with guns or the GAU-22
Shot down 10 enemy air units with the BK-372
Shot down an enemy without auto aim-assist