DeadWing

Okay, here is what you do.

(This is WAY easier if you have the vibration function turned ON. To do that, go to the bookshelf in your room, on the right wall, and examine it. There will be two choices, Takakura's notebook, and Configuration. (I think it's configuration, not entirely sure). Click on the Configuration one, and turn vibration ON.)

First, you cast the fishing rod into the water.
Second, you will get some "miniature" nibbles. These ones won't be really big or really long.
Third, you will get the big nibble. This one will cause some big splashes to appear around the bobber, and you will also get a big vibration from the controller.
Fourth, as soon as the vibration is done, click the X button. You don't need to hold it. For awhile, your character will be pulling against the fish. After that's done, congratulations, you captured a fish.