Here is the full list of all 14 Delta Squad achievements.
As a medic, heal yourself or heal someone else
Kill 50 Engineer soldiers
Destroy a tank
Use your secondary weapon
Complete everything
Starting, complete any level
Find all the hidden loot in any level
Eliminate one of the bosses
Kill 100 Heavy soldiers
Kill 3 enemies with a single grenade
Kill 100 Infantry soldiers
Kill 10 enemies with a single grenade
Survive at least 5 waves in survival mode
Survive at least 10 waves in survival mode