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