Here is the full list of all 21 Firegirl: Hack 'n Splash Rescue achievements.
Receive a medal from the mayor
Complete the tutorial
Rescue your first survivor
Rescue 3 survivors without taking damage
Find the golden cat
Extinguish 200 Fire monsters in a single mission.
Extinguish 10 fire monsters without touching the ground
Break 50 objects in a single mission
Extinguish 100 Fire monsters in a single mission without getting hit
Find the white cat
Find the black cat
Complete a mission with more than 2 minutes remaining
Rescue 1 pet without taking damage
Complete a mission without replenishing water
Seal the Fire Lord
Recruit all firefighters
Purchase the ice axe
Unlock all medals
Purchase the light axe
Survive the first Firelord encounter
Survive the second Firelord encounter