Here is the full list of all 54 Rescue Team: Heist of the Century achievements.
For demolishing a building to building a new one in its place.
For repairing the water extractor on level 16.
For using explosives to remove an obstruction.
For repairing three bridges.
For using the rescue dogs to search ruins.
For using the power pump on level four to drain a flooded area.
For repairing a railway.
For putting out the fire on level 33.
For getting rid of the bats on level 12.
For building 10 hospitals.
For driving away every marauder on level 11.
For acquiring resources via air drop.
For repairing a streetlight.
For removing all of the trash on level 30.
For repairing 40 stores.
For keeping a campfire going
For extinguishing the fires on level 25.
For dispersing a patch of fog.
For chasing away four snakes.
For using the rescue dogs to save the people stranded on the water on level 33.
For stopping the gas leaks on level 29.
For using a lift to save people stranded on a mountain.
For using an airplane to evacuate the victims of the disaster on level 21.
For treating rare animals.
For retrieving the debris from an airplane crash.
For removing every obstruction on level 32.
For repairing a helipad.
For using explosives to remove a block of ice.
For dispatching a boat.
For saving every cat on level two. Be careful! They might scratch!
For repairing five substations.
For finding the first drill.
For removing every lightning ball on level five.
For repairing every lightning rod.
For eliminating every sand devil on level 27.
For repairing a communication tower.
For repairing the warning system on level one.
For launching Dr. Ross' secret assembly.
For cleansing the infected soil on level 19.
For saving the dolphins on level 39 from poachers.
For removing the oil spills in a river.
For planting a grove of trees.
For removing the mold on level 13.
For modernizing an oil refinery.
For using antistactic agent to restore an electrified building.
For finding an Aggressive Electrode that's been programmed to steal.
For stocking the pond on level 36.
For finding a stolen Powereater.
For capturing every stolen Powereater.
For finding 10 showpieces.
For repairing five museums.
For restoring 25 showpieces.
For using the Loader to load 10 showpieces.
For catching 15 quadcopters.