There are 25 Trophies that can be collected.

Bronze

Staten Island
Successfully complete level 1

Military Ocean Terminal
Successfully complete level 2

George Washington Bridge
Successfully complete level 3

Ellis Island
Successfully complete level 4

Protection Camp
Successfully complete level 5

Conversion Tower
Successfully complete level 6

Upgrade
Upgrade a weapon in the Single Player Campaign

Indiscriminate
Kill an enemy with every weapon in the Single Player Campaign

Variety
Use the secondary fire of each weapon in the Single Player Campaign

Dangerous
Kill 50 Chimera in the Single Player Campaign

Silver

Combine
Upgrade both slots of a weapon in the Single Player Campaign

Deadly
Kill 100 Chimera in the Single Player Campaign

Axed
Kill 25 Chimera with Riley’s Axe in the Single Player Campaign

Overheat
Kill 25 Chimera by detonating their heatstacks in the Single Player Campaign

Boom
Kill 25 Chimera with headshots in the Single Player Campaign

Impaled
Kill an Impaler

Executed
Kill an Executioner

Gold

Customise
Upgrade all weapons in the Single Player Campaign

Lethal
Kill 250 Chimera in the Single Player Campaign

Giant
Kill any combination of 10 Impalers or Executioners

Unnatural
Kill the Abomination

Incite
Complete one round of multiplayer

Platinum

Platinum
Earn all trophies

2 Secret

http://www.ps3trophies.com/forums/playstation-trophy-news/16311-resistance-burning-skies-trophy-list.html

I'm enjoying this fun game FPS will be great on Vita.