The Heart of the Machine
Cross Spire to Factory Vent
Video Walk-through
Proceeding across the bridge in shifts under sniper cover makes the trip much less dangerous.
Now that the jammer's out of the picture, your goal is to incapacitate the droid factory and prevent it from making more droid troops. Before you can do so, though, you'll need to cross the interior of the spire to reach a vent leading into the factory proper.
Begin by heading down the hallway near your start point, but don't run into the chasm nearby all willy-nilly. Instead, whip out your sniper attachment and use it to blast any bugs and explosive barrels you can see. Especially important is the barrel near the turret off to the right of the path beyond the tunnel you're in; if you can hit the barrel, the turret will blow as well, leaving you with one less thing to worry about in the battle to come.
Now, the main thing you're going to have to worry about here is the appearance of a Geonosian Elite soldier. These are essentially the Geonosian equivalent of a Super Battle Droid, in that they're much tougher than the normal Geos and pack a much greater punch as well. Instead of a melee weapon, they wield a laser that can quickly cut through your shields and kill you if it gets even just a couple of seconds of unfettered fire on you, so you'll obviously want to keep well away from it! The best solution here seems to be to hang back in the tunnel, walking slowly forward until you can spot the two sniper spots just outside the exit from the same, then task two of your soldiers to those spots before bringing everyone up and focusing their fire on the Elite. There will be other Geos in the area, of course, but the Elite is by far the most dangerous, so try to get it to fire at you, then hide behind the stone pillar between the sniper spots while it blasts its laser at you. There are actually going to be three Elites here, with one popping up after the first one dies, so you may want to task your third squaddie to the sniper spot near the bacta dispenser nearby and use all three of them to destroy the influx of enemies. This is a pretty tough fight, so don't be disappointed if you wind up dying before you get past. If worst comes to worst, try moving forward far enough to trigger the appearance of the Elites, then draw them back into the tunnel at the beginning of the level; they may be a little easier to take down from there.
On the bridge leading across the spire, there are a pair of detonation spots, so start pulling your team off the sniper spots (after making sure that they're all fully healed) and wending your way down the path. There are two barricades to bust through, but there are also a number of sniping spots on the bridge itself, meaning that you'll be able to keep your cover fire up pretty easily as you command your troopers to move up. You'll want to engage in classic bunny-hopping formations, where you send troops forward to sniping spots, then cancel the sniping acts of the troopers furthest to the rear before sending them to the front. Try to make sure that two of your troopers are in snipe position while one of them is moving from the rear to the fore, so that every squaddie that moves has plenty of cover. This also holds true for when a squaddie is placing explosives, of course. If you keep at least two squaddies in sniping mode at all times, then you shouldn't have to fire your gun at all.
Bomb The Tower To Reach The Far Side of the Spire
After the second barricade is detonated, you'll find yourself in a large, open room overlooking another platform with a tower off to the right. There's going to be another Elite popping up shortly, so try to get your guys into position quickly; there are two sniping spots, and a turret off to the left that can be manned, as well as a bacta dispenser for any wounded soldiers, or for yourself if you need it.
When everyone's in place, move out onto the platform until you get a dispatch from Advisor, then back up a bit until you're behind the foremost sniper. In order to move on, you'll have to get someone to place charges on the tower. You can either detach the foremost sniper (who's the target of most of the Geonosian charges) or the turreteer and have one of them place the explosives, but be sure to give them plenty of cover fire, as there are going to be a lot of enemies to deal with here.
When the charges are set, blow the tower to create a makeshift bridge across the spire, then run to the other side to enter the factory.