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
Hire 10 recruits
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
Kill The Justice Minister
Unlock POISON in the Campaign
Kill Cockroach
Successfully complete the first Narcos side-mission
Collect all items on the Intel Board
Complete the DEA Campaign, saving Sandoval
Kill Primo
Successfully complete 10 Kill Shots
Unlock PEÑA in the Campaign
Kill El Mexicano
Kill Poison
10 Kills with SMG
Unlock CARRILLO in the Campaign
10 Kills with Pistol
10 Kills with Grenades
Flank an enemy 20 times
Kill more than 1 enemy in a single Action
10 Kills with Rifle
Kill an enemy using a Skill
Heal 50 health
Start the mission after changing a Unit's Deployment Zone
Gather the Intel and finish the mission
Successfully complete 10 Counteracts
10 Kills with Shotgun
Level up a Unit
Successfully complete the first DEA side-mission
Successfully complete Tutorial
Complete a battle with only 1 Squad death