For this achievement you need to play 150 different songs. The key word here is "different" so you can't just tear through the 25 Blitz songs over and over again.
The most efficient way to expand your song library is through disc exports from previously released games and disc exports of track packs, the largest of these being Rock Band 2. Here's a breakdown:
Rock Band 1 export: 55 songs
Rock Band 2 export: 79 songs (disc export + 9 song bonus tracks download)
Rock Band 2 bonus pack: 20 songs (code included w/ Rock Band 2)
Lego Rock Band: 45 songs
Green Day Rock Band: 42 songs
Rock Band 1 exports easily enough with any copy, but if you're planning on exporting any of the other games or any of the track packs you're going to want to get a new copy if possible. Track packs can be had for very little $ used, but there's no guarantee that the included export code will be usable.
If you're close to having 150 songs in your library and need a short push to get there, four songs are available for free in the marketplace:
"Still Alive" by GlaDos
"Promised Land" by Vesuvius
"Headphones On" by Miranda Cosgrove
"Charlene (I'm Right Behind You)" by Stephen and the Colberts