Gohan goes SSJ2 for the first time against perfect cell. I do not own Dragon Ball Z. I credit it's various owners.
NOTE TO ALL OF THE PEOPLE SAYING THIS ISN'T THE FIRST TIME GOHAN WENT SSJ2:
Technically, you are correct. Gohan managed to transform into ssj2 for a split second in the hyperbolic time chamber. Because the transformation could not be sustained and Gohan had no control over the state, I, personally, don't consider that transformation to be the first time he fully transformed.