You may want to bring a character with an aerial dash along for this mission- there's a timed platform-jumping course later on. Hit the marker outside Aehwa Systems when ready.
A charming cutscene introduces you to Ariadne, and perhaps sheds some light on the Firing Squad episode. When sanity is restored, follow your marker to the first experiment site.
Dispose of the paltry few helltroopers on guard to investigate the bubble- very much the bubbles you've encountered in freeing prisoners from LEGION lairs. As with those, attack the bubble to destroy it.
Follow your next marker to an elevator, which will deliver you into a swarmtrooper ambush.
Clear them out quickly, as there's a bufftrooper commander trotting along after to offer support.
Destroy the three bubbles, then 'secure the area', which involves cutting down another cartload of swarmtroopers. This time they're captained by a shocktrooper.
When all hostiles are down permanently, Ariadne pulls her big trick. Hop on the convenient cargo platform,and hack it to catch a ride.
Hack the marked console at the far end to begin an aerial race to the bubble. You don't technically need aerial dash to finish the course in time, but it helps. Do watch out for Ariadne's dive-bombing drones as you go.
Clear the final, green marker to end the race, then follow your marker to the center of the plaza to summon Gremlin's power booster.
Shoot the booster core to charge it. This works once before LEGION starts jamming you. Follow your marker to the transmitter and destroy it. It is, of course, guarded.
Still, it's just bots. Smoke 'em and return to the booster when the jammer has been destroyed. (it's that same, small four-pronged design from before).
Another burst, and another jammer. This one is guarded by boombots and blitztroopers. The jammer itself is rather charmingly positioned atop one of the cleaning robots (and so is slightly mobile).
Again with the booster and again with a jammer- this one guarded by swarmtroopers and bufftroopers, with the jammer itself concealed on one of the rotating car displays.
Destroy the jammer, and send one last blast through the booster. This will finally pierce the bubble. Bodies hit the floor, a cutscene plays, and the mission ends.