Fatal Fury got 17 remixes (I believe) out of 50 songs. Let's see what I can do.
For the remixes, I mostly focused on the original sequenced tunes. They could do best with a remix!
There may even be some non-AA tracks...

1. (REMIX) Pursuit ~ Cornered (AA)
2. Pursuit ~ Cornered 2001/Variation/2004 Medley (AA)
3. Logic and Tricks ~ 2001 (AA)
4. (REMIX) Cross-examination Moderato/Allegro 2001 (AA)
5. (REMIX) Objection! 2001 (AA)
6. (REMIX) Turnabout Sisters (AA)
7. (REMIX) Theme of Steel Samurai (AA)
8. (REMIX) Pursuit ~ Questioned (JfA)
9. Investigation ~ Middle 2002 (JfA)
10. (REMIX) Pursuit ~ Caught (T&T)
11. (REMIX) Objection! 2004 (T&T)
12. Cross-examination ~ Moderato/Allegro 2004 (T&T)
13. (REMIX) Godot ~ The Taste of Dark-Colored Coffee (T&T)
14. (REMIX) Trial 2001/2004 Medley
15. Truth Medley 2001-2004
16. (REMIX) Pursuit ~ Overtaken (AJ)
17. (REMIX) Apollo Justice ~ A New Trial is in Session! (AJ)
18. Cross-examination ~ Moderato/Allegro 2007 (AJ)
19. Trial 2007 (AJ)
20. Klavier Gavin ~ Guilty Love (AJ)
21. Trucy Wright ~ Child of Magic (AJ)
22. Ema Skye ~ Scientist Detective (AJ)
23. (REMIX) Pursuit ~ Lying Coldly (AAI)
24. Confrontation ~ Moderato/Allegro/Presto 2009 (AAI)
25. (REMIX) Miles Edgeworth ~ Great Revival / Objection! 2009 / Objection! 2011
26. Court ~ Guardians of the Law (AAI)
27. Detective Gumshoe ~ I can do it when it counts, pal! (AAI)
28. Kay Faraday ~ The Great Truth Burglar (AAI)
29. Shi Long Lang ~ Speak up, pup! (AAI)
30. Tyrell Badd ~ The Truth Isn't Sweet (AAI)
31. (REMIX) Pursuit ~ Wanting to Find the Truth (AAI2)
32. Confrontation ~ Moderato/Allegro/Presto 2011 (AAI2)
33. Logic Chess ~ Opening/Endgame (AAI2)
34. Justine Courtney ~ Goddess of Law (AAI2)
35. Raymond Shields ~ Joking Motive (AAI2)
36. The Man Who Masterminds The Game (AAI2)
37. Pursuit ~ Keep Pressing On (DD)
38. Trial 2013 (DD)
39. Athena Cykes ~ Courtroom Revolutionairre 2013 (DD)
40. Simon Blackquill ~ Twisted Samurai (DD)
41. Bobby Fulbright ~ Our Secret Word Is Justice! (DD)
42. Pursuit ~ The Great Turnabout (DGS)
43. Naruhodo Ryuunosuke ~ Objection! 2015 (DGS)
44. Joint Reasoning Medley (DGS)
45. Pursuit ~ Cornering Together (SoJ)
46. Apollo Justice ~ A New Chapter of Trials! 2016 (SoJ)
47. It's show time! (SoJ)
48. Naruhodo Ryuunosuke ~ Objection! 2017 (DGS2)
49. (REMIX) Main Theme (Ghost Trick)
50. The Last Desperate Struggle (Ghost Trick)