The mission begins with 10 turns on the timer and the achievement requires you to finish with more than 3 turns left by the end. Unlike most other missions, this mission doesn’t require you to eliminate all enemies on the map in order to finish, instead, all that is required is the 4 beacons and the train controls be activated. I highly recommend you save your game at the start of the mission so that in the event you don’t meet the requirements, you can reload and try again, otherwise you will need to start a new playthrough.
The method to completing this will depend largely on the type of classes in your squad and your general play strategy but you will need to play offensively. A good strategy is to have 2 or 3 soldiers move up the interior of the train, 1 soldier move up the right hand side and 2 soldiers, preferably one of them a sniper, move up the left hand side or along the top of the train.
The main focus of 1 or 2 of the soldiers inside the train should be to dash to the beacons while only firing on enemies as a last resort or to help thin the herd and using the 3rd to protect the others. The occasional enemy will take up cover inside the train but most will take move to either side allowing you remaining soldiers to engage them. You should be able to activate the first 2 beacons with 7 or 8 turns left on the timer. Some time after activating the 2nd beacon, a muton will show up. (It’s position may vary slightly but will most likely show up on top of the train. If you have a soldier moving along the top of the train, this won’t be too much of an inconvenience. However, if you don’t, then at this stage i suggest moving all your units into the train as a muton with a height advantage can be deadly.
Keeping pushing through the train with at least 1 soldier dashing to the 4th beacon and another dashing for the very front of the train. Once all 4 beacons are activated, use your furthest soldier to reach and activate the main controls. Provided you have 4 or more turns left on the timer, the achievement will unlock.
Overall this is the hardest achievement as it requires you to take some degree of risk and is based on luck of shot outcomes.
TIP: You aren't required to clear all enemies in order to finish the mission, so if an enemy is out of range or doesn't pose too greater threat, leave them and concentrate on the beacons. Also having 6 squad members will make this achievement significantly easier than attempting it with only 4 or 5 soldiers.