This Seeking Tech guide will explain how you can beat Muggshot without taking any damage in Sly Cooper and the Thievius Raccoonus (2024) on PS4 and PS5.
Use the following video as a reference:
When he pulls out his guns, you need to double jump in order to avoid his attack. You can also use the crystals to block the bullets while you attack all the mirrors.
For the second phase, you need to pay more attention to your surrounding when attacking the mirror as you can fall off. Otherwise, make sure to double jump when he pulls out his guns.
For the third phase, attack the mirror up ahead and then wait until he shoots at it. You then need to quickly attack the same mirror again, before jumping diagonally to skip one of the lights. Afterwards, head to the next mirror. If done correctly, you should be able to avoid his attacks.
Do these steps for the rest of the mirrors to end the fight without getting hit.