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.
Complete a mission and land at the airbase with less than 5% fuel remaining
Complete the final mission
Destroy a target using the Grand Slam bomb
Use 'focus' on all 4 gunner stations at once
Complete a mission and land at the airbase with 2 or fewer crew members surviving
Destroy 200 enemy targets
Bail out your entire crew
Defeat all Enemy Aces (in one campaign)
Fully level up a crew member
Fully level up a crew member in two skills
Have one of your crew survive 30 missions
Shoot down a V1 Rocket
Land at the airbase with only one working engine
Defeat 4 Enemy Aces (in one campaign)
Fly 40 missions
Destroy 250 enemy fighters
Fly 25 missions
Destroy 20 enemy targets
Fly 10 missions
Defeat an Enemy Ace
Complete 7 missions with the same 7 crew surviving
Destroy 50 enemy fighters
Sink 5 Submarines
Encounter an Enemy Ace
Repair an engine mid-flight
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