Here is the full list of all 25 Halo: Spartan Assault achievements worth 250 gamerscore.
Earn all Gold stars in Operation F
Earn all Gold stars
Complete Operation F, Mission 4 with the Blind and Thunderstorm Skulls active
Destroy all Mega Turrets with the Grizzly tank in Operation F, Mission 2
Complete Operation E, Mission 1 with the Hollow and Black Eye Skulls active
Earn all medals in the game at least once
Finish the objective without using any vehicles/turrets in Operation E, Mission 4
Finish the objectives using only the Brute Shot, melee and grenades in Operation D, Mission 1
Use every armor ability at least once (excluding Overshield and Seeker Drone)
Kill a convoy target with every stationary gun in Operation C, Mission 3
Prevent all Jackals from regenerating their shields in Operation B, Mission 3
Complete Operation F
Complete Operation E
Complete Operation D
Complete Operation C
Complete Operation B
Complete Operation A
Keep all Wolverines intact in Operation A, Mission 3
Earn your first Gold star
Earn a star of any type
Earn 25000 XP throughout your career
Score a kill with every handheld weapon (excluding Rocket Launcher and Spartan Laser)
Complete any mission with the maximum number of Skulls active
Complete 75 mission specific challenges
Complete all Operation F mission challenges