Vanessa28's advice is spot on. What makes it hard is the speed the other hand moves once you stun one so you just need to act quickly. If using the lens of truth to see the eye is adding another layer of complexity, know that you don't need to use it. Bongo Bongo's eye is always in between the two hands when he charges after both hands are stunned so aiming for the middle with the bow or hookshot will work.
Also a little known trick is that the ice arrows actually are useful in this fight. You only need to hit one hand with an ice arrow to be able to stun the eye rather than hit both hands with regular arrows. However, obtaining the ice arrows is harder for most people than beating Bongo Bongo so this is almost useless.