Hit the marker by the waterfall gate to begin.
After a fun cutscene with Gremlin, follow your marker to a renegade robot dance squad.
The hack here is technically possible, though probably not by human hands.
Either pull off a miraculous unlock, or just fail twice to gain access to the lair below. You'll run through a few empty rooms before facing off against a robo-patrol, which you can run past or annihilate.
The robots in the next room seem to be sending you some sort of message... but they're not, they're just weird. They also attack as you get near the exit, and again you can slay or evade them.
Approach the marker in the next room, then follow it to another jammer/disruptor/corruptor.
Destroy that transmitter and a second one, sweep the room for loot, and be on your way. You'll pass through a series of Ariadne's dioramas- even though some of them seem to have interactive parts, you can't really do anything with them. Ignore 'em, and carry on to a room where you can see Gremlin on a big vid screen.
This begins a loop sequence- locate and destroy a transmitter, survive a wave of enemies, locate the next transmitter, etc. The enemies are always reinforced by boombots, so don't let your guard down. When you've destroyed the final transmitter, a holographic 'cabbit' will lead the way onward.
Follow the cabbit through the next room (you can use 'E' to page it, if you get separated). Pretty much everything in this room explodes as it gets close to you, so shoot everything that makes a move. Avoid these countles mobile mines, and the cabbit will lead you to this room's transmitter.
Destroy it, then journey back to the big screen to finally home in on Gremlin's location. You'll need to jump down an elevator shaft, and wade through some tiresome Alice-In-Wonderland imagery, in order to face off against Ariadne. Well, Ariadne and her doubles. Kill your way through them, focussing on one before moving onto the next. The one with shields-only seems to most often be the genuine article, but just keep up the damage until the cutscene triggers.
In the next phase, you have to grab the three swirling orbs. Do this by intersecting or colliding with them (aerial dash can be an aid here).
When you have all three, drop down to the lower level, and fire up at the tank.
The orbs will reappear, but ignore them. Ariadne can't angle her beam low enough to hit you, so just slowly but surely whittle away the tank health to free Gremlin. Then's it's a final fight with Ariadne.
Barring a few robo-mascots, Ariadne has no reinforcements here, so turrets and other distractions work very well. Keep attacking until her shield goes down. You'll be prompted to lure her into one of her dioramas, but all you have to do is stand in one of the glowing circles until she charges you. Repeat for all three circles, and you'll finally be able to defeat her for good.
Only she escapes completely unscathed in the cutscene (it *is* just like a cartoon). Still, winning the bout recovers Gremlin, and completes the mission.