Here is the full list of all 35 Narcos: Rise of the Cartels trophies - there are 16 bronze, 14 silver, 4 gold and 1 platinum.
Completed all Trophies in the game
Collect all items in El Patron's Journal
Complete the Narcos Campaign, escape into the jungle
Kill A DEA Leader
Destroy the evidence and finish the mission
Unlock EL MEXICANO in the Campaign
Hire 10 recruits
Successfully complete 10 Kill Shots
Kill The Justice Minister
Unlock POISON in the Campaign
10 Kills with Grenades
Heal 50 health
Kill Cockroach
Successfully complete the first Narcos side-mission
Collect all items on the Intel Board
Complete the DEA Campaign, saving Sandoval
Kill Primo
10 Kills with SMG
10 Kills with Pistol
10 Kills with Rifle
Unlock PEÑA in the Campaign
Kill El Mexicano
Kill Poison
Unlock CARRILLO in the Campaign
Kill more than 1 enemy in a single Action
Flank an enemy 20 times
10 Kills with Shotgun
Successfully complete 10 Counteracts
Kill an enemy using a Skill
Gather the Intel and finish the mission
Level up a Unit
Start the mission after changing a Unit's Deployment Zone
Successfully complete the first DEA side-mission
Successfully complete Tutorial
Complete a battle with only 1 Squad death