You'll be in a tunnel with a destroyed Hunter. Head for the doors just beyond it and grab the Magazine just to the left of the doors. This will put you in the lab. When you regain consciousness, you'll be outside and catch a ride from Whitney. When you land on the S-03, you'll be shoved into it's underbelly. Inside, you'll touch the conduits and get shocked. When you come back out of the robot, you'll be back to normal.
Sentries will start coming at you and you'll have to fight them off. When you destroy them, find the Lizard/Connors, on the side by the doors. Go over and help him open the doors. You'll go through and rip something off of the robot. You'll end up back on the back of the robot. You'll have to fight more sentries. Destroy these too and then open the next door. This will immobilize the giant robot.
Smythe
Smythe will have some basic attacks which amout to shooting laser beams in different patterns. You're more than likely going to get hit by these at some point because ther's no room for you to go back, you can't move fast enough to the sides and you can't ascend. The first couple of rounds shouldn't be too bad though.
Shoot at him with your Web Shooters to clog him up. When he tries to hit you, start swinging and you can probably get away for now. Once curls up a little, get behind him and use a Web Rush on his back. This will rip off one of his arms. He's faster now. Do the same thing as you did last time to rip off another arm.
With him down to two arms, he's too fast for you to get away so what you need to do is stand still. When he isn't shooting at you, stand still and shoot at him. When he shoots a beam that moves towards you vertically, move a little to the side and then stand still to shoot at him. Only start swinging when you absolutely must to avoid an attack.
The goal is to stand still as much as possible so that you heal faster. Rather than trying to avoid the damage, it seems better to accept that it will happen and try to heal it. Clog him up and hit him one last time to end the fight.
*Achievement: Tomorrow is Saved