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