In order to earn this trophy, you must have purchased the DLC Colorful Tone song pack.
To obtain this trophy, you must go to the Rhythm Game menu tracklist, press the X button to open the song playing menu, and press the direction pad over until you see the Performance Video menu (PV) and press X again to confirm playing the video for all songs with the Colorful Tone label which is located near the Completion percentage. While the PV is playing, you can press the Triangle button to take a screenshot of the current background of the PV. Also, pressing the X button will pause the video, which is helpful if you're looking to set up a good shot. The Square button will turn the subtitles for the lyrics on and off. After you've taken a screenshot for the PVs in their entirety for 39 unique Colorful Tone songs (you can take more than one screenshot, but for the purposes of this trophy, you only need one per video), the trophy should pop at the end of the 39th PV.
It's highly recommended to do this trophy in conjunction with earning the Music Video Aficionado [CT], which requires you to watch 39 unique Colorful Tone song PVs in their entirety.
WARNING: Do NOT use the Playlist menu to watch the PVs, or it WILL NOT count towards the total. You must watch the PVs from the PV menu in the Rhythm Game tracklist for it to count.