Ordered from earliest accessible to latest. You'll need to find all four of this spider's hideouts so that you can talk to him and earn his sticker/skin. All zone transitions are pretty well obscured by shrubbery so keep your eyes open.

Located in the top right of the zone seen above

Located in the top left of zone seen above

Located in the top middle of zone seen above

Located in the top left of zone seen above

Located pretty high up on the dung hill
Transition to the Robot Spider zone is at the top of the zone seen above after a water segment
Fling yourself up through the zone transition, snag a branch, and you'll find an ant looking for some help in salvaging a robot spider.

This one is located in the skate park most easily accessible from the housing area of the Ant Mound
Located around the middle right of the zone seen above
Blow up the fake wall with your lasers and you'll be able to go up into the Redback's nest and talk to him.

Transition to the Ogre-Faced spider's zone is in the same zone as the transition to the Robot Spider's zone
Transition to the Ogre-Faced spider's zone is at the bottom left of the screen in the water segment
Blow up the fake wall underwater with your lasers and you'll be able to go down into the Ogre-Faced spider's den. Talk to the Ogre-Faced spider 5 times and he'll give you his sticker

There are other ways to access this zone but this is the most intentional way.