[Works on Mobile] Click the breeding structure, then click two monsters. Wait for the monster you bred. Click on it once it has bred then wait for it in the nursery. Once it's done incubating, click on it and you have a new monster! Then you can start breeding all over again until you have them all. You need 3 monsters to unlock the Quatee. You need 7 monsters to unlock the Strinfly. For breeding and incubating, the timer needs to count up to 100 for it to be done. All monsters take the same time.
Credit to @mysingingmonsters for the code Note: I changed Quatee's song for this island I might change this in the future