'Looksmaxxing' streamer Clavicular has a spotlight on him in Florida ... he's under investigation for shooting up a dead alligator in the Everglades.

Lieutenant Governor Jay Collins says the Florida Fish and Wildlife Conservation Commission is looking into the incident.

As we reported ... Clavicular was in the middle of a streaming marathon, cruising through the Everglades in an airboat, when his group came upon a dead gator floating in the water. The streamer then whipped out a handgun and squeezed off a bunch of shots, using the reptile as his target.

Collins is ripping Clavicular, saying ... "Florida's wildlife and waterways deserve respect, not content farming. Under my watch, anyone who abuses wildlife in Florida will be held accountable to the fullest extent of the law."

It sounds like criminal charges could be on the table here ... Collins says, "Looking forward to seeing charges pressed against those who would brazenly disrespect our laws."

A spokesperson for the Florida Fish & Wildlife Conservation Commission tells TMZ... "The FWC is aware of a video depicting individuals in the Everglades on an airboat who appear to be discharging firearms at an alligator. FWC officers are continuing to look into the incident and will provide additional information when available."

Meanwhile, Clavicular was arrested Thursday night in Fort Lauderdale for an unrelated incident ... he had a warrant out of Osceola County and he got hit with a misdemeanor battery charge.