Here is the full list of all 22 Quarantine achievements.
Win without hiring any security operatives
Win without hiring any scientist operatives
Research all tech in a single scenario
Win without hiring any medic operatives
Win before turn 13
Win without hiring any diplomat operatives
Win without any operatives getting below 50% health
Don't fail any operations
Reach maximum level with every operative type in a single scenario
Research a trait
Hire four operatives in a single scenario
Research a tech
Quarantine a city
Succeed at an operation
Win all scenarios on hard
Win all scenarios on normal or higher
Win all scenarios on easy or higher
Win the game from every starting location
Win the game with every leader
Community idea: Win all 5 scenarios without using the "Heal Operative" operation on medium or higher
Community idea: Win all 5 scenarios by hiring only 1 additional operative
Community idea: Win all 5 scenarios after neither treating nor quarantining for the first 3 turns on medium or higher