I made this video that that will sing from your computer speakers to get the achievement. It doesn't do the freeforms, so if you want extra points (which you probably won't need) you can sing them yourself. Use starpower as much as you can. The video will combo the whole song but Guitar Hero has a sketchy vocals engine so it'll only get you about 98%. Also, only the left speakers will be making noise, so don't try it on the right speakers.
Start the video a tiny bit after the first freeform section ends. I realize the audio and video sync is off in the video, which didn't happen until I uploaded it to youtube, but it'll still work just fine
And make sure your lag is set to 0ms, or at least something you can use on your TV. If you're having trouble syncing it up, this might be why.
The video is a recording of me using this method to play the song on expert.