Here is the full list of all 18 Outcasts of Orion achievements.
Complete a run.
Complete 2 runs.
Complete 4 runs.
Complete 8 runs.
Complete 20 runs.
Complete 50 runs.
Complete a +1 run.
Complete a +2 run.
Complete a +3 run.
Get a unit to level 10 or higher.
Win a battle when all but one unit have died.
Win a battle in 6 turns or under.
Win a battle in 4 turns or under.
Win a battle in 2 turns or under.
Have each Freeworld Unit at the same time.
Have each Imperial unit at the same time.
Have each Exile unit at the same time.
Have each Orthodoxy unit at the same time.