Quick continue:
Hold L1 + L2 + R1 + R2 and press Start when continuing to keep the same characters.

Fight as Akuma:
Enter the character selection screen. Highlight Spiral and wait three seconds. Then, highlight the following characters in order: Silver Samurai, Psylocke, Colossus, Iceman, Colossus, Cyclops, Wolverine, and Omega Red. Finally, highlight Silver Samurai, wait three seconds and press LK + HK + HP. Akuma will appear in place of Silver Samurai to confirm correct code entry. To fight as Akuma as player two, highlight Storm and wait three seconds. Then, highlight Cyclops, Colossus, Iceman, Sentinel, Omega Red, Wolverine, Psylocke, and Silver Samurai. Then, highlight Spiral, wait three seconds, and press LK + HK + HP