This game without even considering DLC songs has 110 songs on it (including on disc GH tracks) so you only need 5 songs more.
DLC is no longer available for this game now (as of April 2014) so you have to download GH tracks to get this now.
GH tracks is under "Create" then "GH Tracks"
Once you download enough tracks (make sure you press Yellow to save them after downloading the preview).
Once you go into Quickplay+, the trophy will pop at the song selection screen provided the number of songs counter displayed at the top is 115 or more.
Alternately, if you don't want to download tracks from GH Tracks, you can create your own using GH Mix or GH Jam, also on the "Create" menu.
This can be a good alternative should the GH Track servers ever get pulled or are down for whatever reason.