This is a rhythm game speedrun with the only basis being that you complete charts, unfortunately nothing too fancy but there are a few things you can do to speed it up compared to a regular playthrough.

1: You can only do the last tutorial and the first playlist unlocks.

For this you just want to go into the tutorial playlist after starting a new file, edit the playlist, and uncheck everything except the last tutorial. Play that as normal and you'll be good to go. You could also just not edit the playlist and skip every tutorial (except the last one cause you can't) once you get into the game but editing the playlist is much faster.

2: Restarting songs between transitions skips the freestyle part.

Unfortunately like most Guitar Hero games, you can't skip the venue opening cutscene if it's the first song you play with restarting the song... because you can just skip it normally by pressing any button. Restarting the song is ONLY used for transitions to the next song with the turntable only, due to it skipping the freestyle part. You can't do this on Wii, because for some reason the venue opening cutscene starts playing again and it is unskippable this time. Every other version is not like this. However, you can do this on DJ Guitar songs, but there are no freestyle parts, so you would be losing time instead compared to not restarting it at all.

3: Using the quickplay playlists to select songs rather than using the normal playlists.

This mainly saves time on menuing and time spent dealing with the ending cutscene on songs. I don't really have much else to add to this part, this one should be obvious.