The Kelp avatar is quite elusive, therefore one of the most coveted random avatars. It is expensive, it is tedious, it is repetitive. This method has been tested time and again. The most tries I have seen using this method has been 13. It will cost you 60,400 neopoints per try. I compiled this guide (and then re-did it) in the hopes that I will help others achieve this expensive and annoying avatars. Please let me know when you get the avatar and how many tries it took you!
This is the page you are presented with when you enter the restaurant. It is also the page you get when you click on "Waitress". Each of the sections listed contain a food for you to choose. You will choose a food from each section, and the last is the "Eat" screen where it lists all that you ordered for your pet.
The first thing you need to do is get your *LIGHTEST* pet as bloated as possible. If they are in the neolodge, let them get up to bloated and then take them to the movie theater and feed them until they are "very bloated". Then take them to the restaurant.
Alternative strategy:
Credit to @(you need an account to see links) for this information!
I've had many successes getting leftovers from both kelp and golden dubloon by feeding items to lupe, skeith, jetsam, and grarrl. Usually get leftovers with these pets every 4 or 5 tries. Being bloated before going to the restaurant didn't seem to effect the leftover rate (got leftovers on a lupe that was dying). Other pets had a lower percentage, I also tested Ixis, meercas, zafaras, draiks, and acaras and they had a shitty percentage compared with the other pets. I haven't tested all pets but I do believe that a lupe is the best pet to use to get leftovers. One lupe I fed so much that he was very bloated for an entire month. I was trying for gourmet foods at GD and definitely got leftovers every 5th attempt at most, sometimes faster. Below are the cheapest foods available at the Kelp restaurant. Don't bother buying the expensive ones as WHAT they eat has no effect on your chances of receiving the avatar. They are listed in order.
Please note that you may not get a notification that you have recieved the avatar. Do not close your screen yet, check you avatars. If you did not receive it, refresh the page a few times. If you did not get it, try again. If you still don't get it, try this method with a different pet.