Here is the full list of all 24 Bedlam achievements worth 1,000 gamerscore. It takes around 6-8 hours to unlock all of the achievements on Xbox One.
Complete Star Fire
Score more than 3500 points in Rescue Run
Completed Rescue Run
Reach the end of the Boulevard du Burnistoun
Complete the secondary objective
Escape from Age of Attrition
Hope Springs Eternal
Secure Sigma Sector
Mess with the Valve
Complete the Graxian combat training and salute your commanding officer
Complete the Game
Find the Fire Sword
Defeat Lanzok and free the captive marines
Kill 5 opponents in the Arena without dying
Reach the end of the Rue de Chambard Rouge
Bring down the Super Saucer
Encounter the Accounts Dept.
Destroy the Armoured Car
Complete Planetfire Ascension
Defeat the horde
Destroy the Gaian Comms Jammer
Clear the Chilli Chomper Maze
Destroy all three guard towers in Death's Dark Vale
Complete Rage-Quit Reactor without the Reactor exploding