Climb the giant robot was a mission in The Precursor Legacy that Jak and Daxter completed to obtain a power cell. The Precursor robot the Lurkers were excavating in Spider Cave had a lone power cell located at the very top, until Jak managed to reach it.
When entering the second cavern in Spider Cave you will encounter a large Precursor robot surrounded by scaffolding occupied by driller lurkers and babaks. The way to the top is difficult, with many platforms that drop when you stand on them, grills that release hot jets of flame into the air, and rock-crushers. Moving towards the robot you will find a ramp leading to the first level of scaffolding.
While going through the various obstacles here you will eventually want to go right use the elevator in the corner to get to the second level. More obstacles block your way as you traverse the wooden scaffolding, ultimately directing you to the other side of the cave where you will find yet another elevator to bring you to the third level.
Here you will find additional obstacles as the camera angle ends up shifting to a 2D side-scroller view. You will have to swing past many dropping platforms, gaps and grills using the many poles here. Ultimately you will end up on a wooden platform right above the Precursor robot where you will find the power cell.
It is important during this mission to navigate carefully and patiently, as a single fall has the potential to make you restart at the very bottom. Do not concern yourself too much with hit points as there are several green eco clusters which can replenish your health before you die if you are nimble enough. The driller lurkers impede mission progress the most as they will often walk your direction and pause for several seconds before turning around making them vulnerable to attack. Be patient and strategical, and you will reach your destination.