Here is the full list of all 34 Narcos: Rise of the Cartels achievements.
Kill a DEA Leader
Collect all items in El Patrón's journal
Complete the Narcos Campaign, escape into the jungle
Destroy the evidence and finish the mission
Unlock El Mexicano in the Campaign
Collect all items on the Intel Board
Kill the Justice Minister
Unlock Poison in the Campaign
Complete the DEA Campaign, saving Sandoval
Kill Primo
Kill El Mexicano
Unlock Peña in the Campaign
Kill Poison
Unlock Carrillo in the Campaign
Kill Cockroach
Kill more than one enemy in a single Action
Hire 10 recruits
10 Kills with Grenades
Successfully complete the first Narcos side-mission
Heal 50 health
10 Kills with the Pistol
10 Kills with the SMG
Kill an enemy using a Skill
Flank an enemy 20 times
Successfully complete 10 Kill Shots
Gather the Intel and finish the mission
10 Kills with the Rifle
Successfully complete 10 Counteracts
Level up a Unit
10 Kills with the Shotgun
Start the mission after changing a Unit's Deployment Zone
Successfully complete the first DEA side-mission
Successfully completed the Tutorial
Complete a battle with only one Squad death