I don't have the game on PS2 or Wii, so I can't confirm if they work there.
You can do the 1st glitch for Crime Waves in 3 ways:
1. Press Triangle during the fail animation, as shown in the video.
2. Press Triangle during the initial transformation animation, you have to be quick.
3. Press Triangle during the de-transformation success animation. This gets harder/undoable because you will be mashing Triangle to de-transform later on.
For the 2nd glitch against The Lizard, this is solely beneficial for a speedrunner, not a casual player. Buying the jump upgrades helps, but this is one of the early missions in the game, so you'll need to spend your Hero Points on them before the other upgrades.