Here is the full list of all 20 Discharge achievements.
Pass Mission 1 in Campaign
Pass Mission 2 in Campaign
Pass Mission 3 in Campaign
Pass Mission 4 in Campaign
Pass Mission 5 in Campaign
Pass Mission 6 in Campaign
Pass Mission 7 in Campaign
Pass Mission 8 in Campaign
Pass Mission 9 in Campaign
Pass Mission 10 in Campaign
Kill an enemy while playing as APC
Kill an enemy while playing as Tank
Kill an enemy while playing as Gunship
Kill an enemy while playing as Bomber
Fuel an ally using E-Transmitter in third person mode
Capture Iridium Mine in third person mode
Personally slay 20 enemies in a won match
Win a custom match
Play 60% or more in third person mode in a won match
Play 5% or less in third person mode in a won match