Just did this on my solo run and didn't get the achievement. As I don't remember from playing it numerous years ago I forgot you have to do it specifically or else you don't get it.
Item of note just in case: You can use the tank from a distance to destroy the anti-air instead of going inside to blow up the reactor. Saves a bit of trouble.
Taken from the 360 guide by your fat uncle:
"This is a bit misleading. You do not have to finish the mission to get it, you just have to drive the tank, not blown up into the "parking space" that is the entrance to Sword Base where you got the orbital gun earlier in the game. If you (as I did) leave the tank where you found it and go on to finish the mission without bringing it to the gate, you will not get the achievement."
Additional note: I got the achievement when I brought the tank to the gate. You do not need to finish the mission.