Here is the full list of all 23 Into The Flames achievements.
Completed The House Fire level
Completed the Warehouse Fire level
Completed the Farm fire level
Completed the academy
Rescue a downed Firefighter
Put out a fire
Ventilate a Roof
Rescue a Victim
Break a door down
Force open a door
Find the Golden Mayo bottle on the county map
Connect a supply line to a hydrant
Die
Recover a hazardous barrel
Shut off a hazardous valve
Find the Golden Mayo Bottle on the city map
Cut down a tree
Take command of an incident
Change your role at an assignment board
Manually place an incident under control
Put out a car fire
Transport a patient to the hospital
Parachute out of a helicopter