Here is the full list of all 34 Narcos: Rise of the Cartels achievements.
Collect all items in El Patrón'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
Unlock Peña in the Campaign
Kill El Mexicano
Kill Poison
Kill more than one enemy in a single Action
Unlock Carrillo in the Campaign
10 Kills with the SMG
Hire 10 recruits
10 Kills with the Pistol
10 Kills with Grenades
Heal 50 health
Successfully complete 10 Kill Shots
10 Kills with the Rifle
10 Kills with the Shotgun
Gather the Intel and finish the mission
Flank an enemy 20 times
Successfully complete 10 Counteracts
Level up a Unit
Kill an enemy using a Skill
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