Hooks for floating shelves
For that much weight, I would try to drill into the studs. You can find them using a studfinder, or sometimes knocking and listening for the change in pitch will be enough. If in doubt, find several, and assume they are evenly spaced. Make sure the drilled holes and screws are long enough to penetrate well into the stud, say at least 2 inches.

Of course, to do this, you need to be able to adjust the distance between the screws to match the distance between the studs. If, for whatever reason, this isn't possible, you can use a small board as an interface. Cut a narrow board long enough to span the studs, or the length of the shelf, whichever is longer. Screw it into the studs. Then use short screws to attach the shelf to the board.