How to open this air return duct between joists
The thing that runs perpendicular to the duct sheeting looks like a standard z folded clip. Not sure of the mechanism of the sides, but they are probably simple slots.

After laying plastic sheeting on the floor and donning a dust mask and gloves, I'd try simply shoving the bottom of the duct upwards. It should buckle and come apart, dumping everything onto the floor below. 

Re-assembly is probably easier if you use sheet metal screws and foil tape.