Here is the full list of all 31 1943 Deadly Desert achievements.
Destroy an enemy command unit
Destroy 15 enemies with the command unit
Use the "Mount!" ability 20 times
Position infantry in trenches 20 times
Discover 50 enemies with planes
Destroy multiple enemies with an attack of the medium bomber
Have 7 different tanks at the same time
Destroy an artillery unit while too close for it to counterattack
Destroy 15 enemies with parachuted infantry
Find 30 enemies with radar
Destroy 75 enemies while being buffed by the command unit
Use abilities of the Axis engineer 200 times
Destroy 75 enemy planes with fighters
Destroy 50 enemy tanks with tank destroyers
Destroy 100 enemies with hybrid artillery
Attack with artillery 200 times
Move infantry over 1500 tiles
Use the "Fortify" ability 250 times
Win 10 online battles
Finish the campaign "Assault on Deep Sand"
Finish the campaign "A new Threat"
Finish the campaign "Wasteland Warfare"
Finish the campaign "Unforgotten"
Capture 500 enemy buildings
Reach the highest rank
Win 100 online battles
Reach the prison in the mission "Heroes" through the front entrance
Finish the campaign "Strong Winds"
Finish the campaign "Daybreak"
Finish the campaign "Behind Enemy Lines"
Finish the campaign "Survival of the Fittest"