I went to Games and completed it, yada yada. But how do I go to the Island and get Hydrus pets? Also, do you just get one Hydrus pet per map?

The map allows you to go the island that is east of the fairgrounds.

Once at the island, you click on the Merana link you will get a list of pets you have which can be made Hydrus, click on the one you want and she will give you a quest (she asks for a ramdom set of ingredients). Once you have the ingredients in your inventory she will make your pet hydrus. You can repeat this any number of times to make however many pets you want Hydrus.