Here is the full list of all 13 Dropzone achievements.
Kill 100 enemy Rigs.
Win a Dropzone match.
Upload 3,333 cores.
Participate in 1000 matches.
Kill 75,000 Kavash units.
Destroy each Hive on the map at least once in a 2v2 match.
Earn a total of 50,000 Jovians.
Destroy an enemy Rig while it's healing in its dropship (PvP).
Root an enemy Rig, and then destroy it while it's rooted.
Team Wipe the entire enemy team in a 2v2 match.
Destroy an enemy Rig with the Tank ability "Landfall".
Cancel an enemy Rig's channeled ability with a silence.
Upload 36 cores in a single match. (PvP)