There are 10 new Trophies in this DLC.

Bronze

Air Superiority
Clear a safe path to the Terraformer for Hale. (Downloadable Content)

Bird of Prey
Allow no Red Faction to survive your attacks on their mountain base. (Downloadable Content)

Swath of Destruction
Reunite Sgt. Winters with the Red Faction. (Downloadable Content)

Armored Cavalry
Rescue the pinned-down Red Faction soldiers. (Downloadable Content)

Nuke It from Orbit
Wipe out the Cultist military camp. (Downloadable Content)

Wrecking Ball
Get 20 kills with the Shard Cannon. (Downloadable Content)

A Taste of their Own
Eliminate 10 enemies using one of their own turrets. (Downloadable Content)

Stick Around
Get 20 kills with the Sharpshooter. (Downloadable Content)

Full of Malice
Kill Mallus. (Downloadable Content)

Silver

Triple Threat
End the three-way battle between yourself, the aliens, and the Cultists. (Downloadable Content)

http://www.ps3trophies.com/forums/ps3-trophy-news/64646-red-faction-armageddon-path-war-dlc-trophy-list.html