SNES Advance is an SNES emulator for the GBA that doesn't run very many games at full speed. In order to make games run faster, the creator allowed for users to create speedhacks for specific games. Games run at a fixed 60 fps, so when all the work is done in a frame it sits in an idle loop until the next frame comes along. By finding the loop and skipping it, we increase speed. Lots of users then went out and found speedhacks for a ton of games, compiling them into a single database called snesadvance.dat. The SNES Advance builder tool reads this database file and applies the speedhacks as it creates the *.gba binary.
SNES9X for the PSP decided to use this database to increase speed, since all the hard work had already been done to create the database in the first place. It ignores some of the fields that are specific to SNES Advance and uses only the speedhacks themselves.
I recently speedhacked some games that have no chance of running in SNES Advance but do run in SNES9X TYL like SMRPG, Kirby's Dream Land 3, and Yoshi's Island, among others. I've requested that they be put in the official snesadvance.dat file available at the PocketHeaven forums, but he hasn't updated it yet. The above patch for Chrono Trigger is from a separate list made for Snezziboy, a different SNES emulator for the GBA that also uses speedhacks.
When you downloaded SNES9X TYL you should have gotten an snesadvance.dat file. It's probably outdated, but that's beside the point. Open it with Notepad, turn off Word Wrap, and add the Chrono Trigger entry, replacing an old one if it's there. Then try CT again to see if it helped any. As I don't have a PSP myself I don't know exactly where this snesadvance.dat file is supposed to go, sorry.