This quest seems awfully buggy at the moment so here's a guide on what to do. Once you pick up the quest stay in the area and a large red circle should appear on the floor near you dropping your exile battle suit which you can right click to enter. Stay on the main road and kill the guys needed, avoid going off to the sides as it may dismount you. If this does happen you need to abandon the quest and return to Commander Durek at Stonebreaker's Stand to pick the quest back up as it refuses to drop a second exile battle ship currently.

This quest is not bugged at all. Just stay around the road (The Sunder Flat). When the road will end and you'll try to go further (Shatter Ledge or Behavioral Research Facility 394), you will get notification and will get dismounted. It basically tells you that "You left the area. The battlebot will explode in... 3... 2... 1...". You cannot complete this quest by killing mobs by hand, not even after already using the robot. And only way of finishing this quest after getting dismounted too early is.... abandoning the quest and running all the way back to Durek and then back to quest area again.

Couldn't find a way to edit my post but after being repeatedly dismounted you can resort to killing them the good old fashioned way once you've accessed the suit once.