A short Beastie Bay Boss Taming Guide to help shed some light on things. At first most of the bosses found in battles wont be able to be tamed until you purchase a certain item. You can however collect a few enemies that are bosses in the early game with the item.
After completing the desert island you will find a person who’s house will turn into a store called Wairo Inc. Inside this store you will find several settings and game features that can be unlocked for the price of gold. One of those features is the ability to capture bosses. You should purchase this as soon as possible if your hoping to catch some good allies. Bosses will usually be the best kind of allies that you can find, though some normal enemies are good though only a few.
To tame a boss you will usually need to feed them multiple times unless your bait is of high quality are is the correct element type. Sometime they will like the food the dislike it when given again. This is when you can just keep trying with the same food or try something that has a matching element.
Catching a boss is almost a must and you should try to catch as many as possible especially the ones towards and at the end of the game. When you start a new game you can take one allie with you from your previous game if you purchased the option at the Wairo Inc store. If you plan on playing again to get a higher score or just to keep playing you should try and get the best allie possible in your first playthough and that would definitely be one of the bosses. Since each boos will have a different element many of them are useful for different situation and making them useful in the right situations even if their stats aren’t as high as others.
If you want more related info on this app your can check out the Wiki here.