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