Rock Band 3

All Rock Band DLC and Rock Band Network songs work for this achievement.

List of free songs you could use for this:
(click any song for download link)

GLaDOS - Still Alive
Lights Resolve - Dreaming of Love
Little Fish - Am I Crazy
Miranda Cosgrove - Headphones On
Stephen and the Colberts - Charlene (I'm Right Behind You)
Various Artists - Rock Band Network Megamix 01
Vesuvius - Promised Land

A few of the above songs may not be available in some countries.

Rock Band Free Pack 01:

Abnormality - Visions
Anarchy Club - Get Clean
Bang Camaro - Night Lies
Breaking Wheel - Shoulder to the Plow
Libyans - Neighborhood
The Main Drag - A Jagged Gorgeous Winter
Speck - Conventional Lover
The Sterns - Supreme Girl
That Handsome Devil - Rob the Prez-O-Dent

20 Song Bonus Pack (requires purchase of NEW copy of Rock Band 2):

The 88 - Sons and Daughters
Authority Zero - No Regrets
Between the Buried and Me - Prequel To The Sequel
The Cab - Bounce
Chevelles - Get It On
The Cocktail Slippers - Give It To Me
Dealership - Database Corrupted
Endeverafter - I Wanna Be Your Man
The Ghost Hounds - Ashes To Fire
Hollywood Undead - Young
Kutless - The Feeling
The Len Price 3 - If I Ain't Got You
Lesley Roy - I'm Gone, I'm Going
Opiate for the Masses - Burn You Down
Semi-Precious Weapons - Magnetic Baby
Shaimus - Like a Fool
Thenewno2 - Crazy Tuesday
Tickle Me PinkThe Time Is Wrong
Underoath - Desperate Times, Desperate Measures
X Japan - I.V.

If you don't already have enough DLC for these achievements I recommend doing all of the other DLC achievements first. Several of them require specific songs or songs from certain lists, so you'll end up getting much closer to 20 songs by the time you finish them. New copies of the various track packs (AC/DC, Country, TP2, Metal, etc) can also all be exported for free from any non-used copies. Any of them would give you more than enough songs for this achievement.