The little spidery thing with two white eyes & long wispy legs? On the opposite branch? You 'grab' the end of the leg that's not attached to the branch it's on & stretch it over & 'fasten' it to the branch our heroes are on so they can cross over on it.
If you mean the big beetly spider that comes flying down & chases them back when they're halfway across, you need to have the 'trumpet beetle' in your inventory to get rid of it... the 'trumpet beetle' you got in the sleeping bat sequence.
Good luck!