Here is the full list of all 30 Bomber Crew achievements. It takes around 25-30 hours to unlock all of the achievements on Windows.
Have one of your crew survive 30 missions
Shoot down a V1 Rocket
Destroy 250 enemy fighters
Fly 25 missions
Defeat 4 Enemy Aces (in one campaign)
Use 'focus' on all 4 gunner stations at once
Destroy 20 enemy targets
Complete 7 missions with the same 7 crew surviving
Fly 10 missions
Sink 5 Submarines
Destroy 50 enemy fighters
Defeat an Enemy Ace
Encounter an Enemy Ace
Complete a successful mission with all 7 crew surviving
Return to the airbase having successfully bombed all targets
Land at the airbase with only one working engine
Complete a mission and land at the airbase with less than 5% fuel remaining
Destroy an enemy target
Repair an engine mid-flight
Take a photo of an intel site
Complete the first mission
Bail out your entire crew
Destroy 200 enemy targets
Complete a mission and land at the airbase with 2 or fewer crew members surviving
Destroy a target using the Grand Slam bomb
Fully level up a crew member
Fully level up a crew member in two skills
Fly 40 missions
Defeat all Enemy Aces (in one campaign)
Complete the final mission