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