This Trophy is for maxing out your grip gauge. It can be done in either the Tanker or Plant chapters of the game, though you'd probably be better off doing it in both. To increase your grip gauge, you need to perform "pull ups". These are done by standing next to a railing with an overhang, pressing the triangle button, and then using the rear touchpad to "pull yourself up" so that your head is level with the floor.
This can be done on just about any railing in the game, but I'd advise you to wait until you reach the Engine Room section of the game before giving it a legitimate shot. The area is big, there aren't many enemies, and the lack of rain means you won't get sick while working on this.
Upon entering the room, you'll need to take out any enemies on the top floor, and any who might be walking past on the floor below (numbers and positions vary by difficulty). It's up to you whether you want to kill them or just knock them out. Keep in mind that if you knock them out, you'll have to keep reapplying tranquilizer to each of them as it wears off.
With any nearby enemies neutralized, stand next to the railing on the top floor and press the triangle button. Now comes the tricky part. Take the middle fingers on both of your hands and press them firmly against the middle of the rear touchpad. Now slide them down. Make sure there isn't a significant pause between pressing against the screen and sliding down. If you've done the move correctly, you'll see Snake pull himself up so that his head is level with the floor. Now release your fingers so you go back down, then repeat the process until you're almost out of grip. In my experience, you can get about 3-4 pull ups before running out on Level 1 Grip, and 7-8 on Level 2.
You'll need to perform 100 pull ups to reach the next level, meaning 200 in total. You'll know you've reached the next level when you see your Grip gauge change color, and you receive a call from Otacon telling you that you've gotten stronger.
All things considered, this is only slightly less annoying than dodging lightning 100 times on the Thunder Plains in FFX. Especially due to the lack of L2 and R2 buttons in this port. Good luck!