We prototyped this and learned a couple things that I'm happy to pass along.
1. Bimba sells double-wall cylinders that go much longer than the standard 24" that the singles do. They weigh slightly more, but since it's lifting the robot, I would've considered putting the cylinder in a tube to protect it anyway. 6.7 lbs for a 36" we bought on ebay.
Here's a 28" for sale on ebay today.
http://www.ebay.com/itm/BIMBA-DWC-6028-2-DOUBLE-WALL-PNEUMATIC-CYLINDER-2-1-2-BORE-X-28-STROKE-/151469157440?hash=item234443ec40:g:X30AAOSwrx5UXm0 g
2. a 2-inch cylinder on pull (subtract out the shaft area) can lift about 170lbs at 60 psi. Don't forget that your 120 lb robot has a battery and bumpers. Also, the friction of the bumpers dragging against the tower will be significant, based on your bumper design and the placement of the lift-point on the robot. We lifted a very heavy older robot (150lbs?), but we had to go to 65 psi to actually climb the wall with a 2-inch cylinder. Not doable there.
3. Yes, we had two black tanks and they emptied in the first six inches. But the overall lift powered by a Thomas compressor still finished in the 20 seconds. More like 15 seconds.