I picked this one up today and it was easier than I thought. Here are the earliest starting missions for each Armor Ability. You do not need to complete the level for the ability use to count.
Regen Field - A-1
Sprint - A-3
Stun Blast - B-1
Hologram - B-4
Active Camouflage - C-3
Hardlight Shield - D-2 (Earliest pickup of this item is Mission C-4)
Autosentry - A-1 (Must be purchased for 300XP, does not occur as starting ability)
Simple enough: start up each level and use the starting Armor ability once and you will get the achievement as soon as the last ability is activated. Easy 10G!