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