I actually found this to be one of the simpler rainbows.
Red Honey
Grow many red flowers and any red flower that has a bee hovering over it will produce red honey.
Tuna
Very simple the tuna can be caught mainly on East Gull Island.
Perfect Honeydew
You can do one of two things
Chat with our AI personalities
you have to complete the first rainbow (green) and then talk to the captain in on the hook
Go togamefaqs.com to see the answer they have lots of answers for that one.
By completing the first rainbow.
Once you get Alan's rainbow, go on it. You will be at the top of the mountain. Walk to the left and you will find his tree.
first you have to have completed darens rainbow, if you havn't, then do it, after you have done that you need to go over that rainbow to get to gull island where you meet the harvest sprite named collin. you then have to complete his rainbow (it is kinda complicated) and cross his rainbow, then you arrive on the other gull island. from there walk along the beach where a cutscene should appear, you should get the badge in that cutscene... Hope i helped!!!!