In the first few tries I had some real difficulty trying to get through this mission, but I found that it can be won fairly easily, if you enter the bomb-room from both sides. Just getting there was a dangerous path, with those patrols moving about in the tunnels.
A good trick is to get to the first bomb on the west side of the room before the enemy can get there to arm it. If the first bomb is armed, then the time limit starts and I think you only have 3 turns to resolve the situation. That could be why the building blew up even though you disarmed the last bomb, seemingly in the nick of time, only to find out the building blew up on you anyway...
Entering from both sides of the room, and getting into the right position near that first bomb will stop the enemy from arming it, which stops the 3 turn time limit, and doesn’t cue the cut-scenes of the enemy arming a new bomb each new turn. Once I had my team use the tactic of converging from both sides, I was able to finish this level, using just grenades and standard weapons. :)