There are an infinite amount of lizards crawling around in the game, but only 77 shining lizards. You can easily identify a shining lizard as its tail is white and not black like the rest of its body. Unlike the normal lizards, these ones prefer to hide and so it can be difficult to track them down. This is much easier to do once you beaten the main game and obtained the Lizard Detection Stone from the Time Attacks. You must kill all 77 of the shining lizards in a single playthrough for this trophy.
See the Shining Lizard Guide for specific details.