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.
Fly 25 missions
Destroy 250 enemy fighters
Complete 7 missions with the same 7 crew surviving
Shoot down a V1 Rocket
Defeat an Enemy Ace
Destroy 20 enemy targets
Fly 10 missions
Sink 5 Submarines
Destroy 50 enemy fighters
Repair an engine mid-flight
Encounter an Enemy Ace
Complete a successful mission with all 7 crew surviving
Return to the airbase having successfully bombed all targets
Destroy an enemy target
Take a photo of an intel site
Complete the first mission
Bail out your entire crew
Destroy 200 enemy targets
Land at the airbase with only one working engine
Have one of your crew survive 30 missions
Complete a mission and land at the airbase with less than 5% fuel remaining
Complete a mission and land at the airbase with 2 or fewer crew members surviving
Use 'focus' on all 4 gunner stations at once
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 4 Enemy Aces (in one campaign)
Defeat all Enemy Aces (in one campaign)
Complete the final mission