Well i just unlocked this achievement, you should get it while trying for the item achievement. here are the BGMs and where they are found
1. Selection- when you unlock your first dragonball in Galaxy Mode
2. Cosmic Battle- Somewhere in Galaxy
3. Space Museum- Somewhere in Galaxy Mode
4. Online Fighters- Somewhere in Galaxy Mode
5. BUDOKAI- Somewhere in Galaxy Mode
6. Battle of Omega(Guitar Solo)- the first time you summon Shenron
7. Battle of Omega(Full)- First Time you summon Porunga
8. The Great Expectation- Goku's Galaxy
9. Challenger- Bardock's Galaxy
10. Soldier's Sorrow- Goku's Galaxy, i think in the fight with vegeta scouter.
11. Speedster- Frieza's or Goku's, when they fight each other ssj and 100%
12. The Dawn of The Extreme Battle- One of the Ginyu Force's Galaxies. Probably have to beat them all
13. Get Out- I think you have to beat android 19 and 20's Galaxies
14. Force of Justice- In either Gogeta's or Janemba's Galaxy. i think Gogeta's.
15. Pathos- im pretty sure it's Majin Vegeta's. when he fights Goku
16. Gallant- Adolescent Gohan's Galaxy
17. Ultra Energy- Broly's galaxy i think
18. Dangerous Zone- Either Cell or Teen Gohan's Galaxy
19. The Hero- Trunks(Fighting Teen) Galaxy
20. Brave- Trunks(Sword) Galaxy or Mecha-Frieza's
21.Yin-Yang- Teen Gohan's, in the Fight with adolescent Gohan
22. Rivals- Kid Trunks or Kid Goten's Galaxy, in the mission where they fight each other.
23. The Strong Enemy- Gotenk's or Super Buu's Galaxy. when they fight each other
24. The Anthem of Lives- Turles' Galaxy, in one of the side missions
25. Accelerator- Cooler's Galaxy
26. Weird Atmosphere- Meta-Cooler's Galaxy
27. Nose to Tail- Android 13's Galaxy
28. Katharsis- Bojack's Galaxy
29. Harlequin- Super Janemba's or Goku's Galaxy. when they fight each other most likley
30. Defiance- Probably Adolescent Gohan, Videl's, or Broly's Galaxy. i cant remember i had this one for a long time
31. Critical Power- Teen Gohan's Galaxy
Hope this helped. you should easily get this while going for all items. You might also unlock a few in batttle/ultimate zone or world tornament/cell games. i beat all battle and ultimate zones, and the world tornament and cell games on hard, so you might have to do that too. Good luck.