I've found some lovely Bladed Rhino Beetles and Electric Rhino Beetles and travelling merchant and noted insect enthusiast (and arrow extortionist) Beedle, who hangs out at the various stables around Hyrule, has gone nuts for them and likes to demand that I trade them to him. He's offered a (fairly weak) Mighty Elixir, or some food. Is this a good trade? Will he offer any further rewards if I give him enough Beetles? Or should I hold on to my bugs?
15 Electric Rhino Beetles are used for upgrading some particular pieces of equipment. See below for end game spoilers:
The 'of the Wild' armour set, unlocked by completing all 120 Shrines.
Other than that, there are no other uses for Beetles. So feel free to give them to Beedle to make him happy, or keep them for making elixirs. The reward from Beedle doesn't improve beyond a relatively low strength Mighty Elixir.
Sure, give him your beetles!
From my observations, Beedle will take one beetle per ingame day and give you an elixir or meal in exchange. I have given him around 10 beetles so far and haven't received anything twice from him. In my opinion, it is well worth to get some nice random elixir or meal. On a different note, it makes Beedle really exstatic.
Of course you can keep the beetles and make elixirs, but you could also use butterflies or lizards.