The three "Air Strike" achievements are cumulative both through the Gaea campaign and the strategy game. To destroy a Walrus using a Manta, you must be controlling a Manta directly and shoot the final shot that destroys a Walrus controlled by the enemy AI. Any Walruses that are destroyed by your carrier, turrets, or vehicles that you are not directly controlling do not count for these achievements.
I would suggest completing the campaign first as you will need to destroy a lot of them to finish that. In a strategy game, invade an enemy island, starting by destroying any anti-air turrets and enemy Mantas. When you see a group of multiple enemy Walruses, save the game, destroy them, then reload the save. Using a Manta armed with rockets or missiles will make this go much faster. Rinse and repeat until you have 1000 kills, at which point the achievement will unlock.
If you choose to do this in the campaign, you first gain a Manta after capturing Treasure, so the first point at which you can earn the "Air Strike" achievements is when attacking Frontier (the fourth island in the campaign. Note that the three "Bug Crusher" achievements will be unlocked by completing the requirements for the "Air Strike" achievements.