It only works on the PS2 version, not the PSP version.
On the PSP, you can't catch a monster whose level is higher than Adell's or Axel's.

In the PS2 version, you could catch monsters whose levels were about 2 to 2.5 times higher than your highest-level character. This meant that you could go to the Dallos River: Red Waterfall stage, wipe out all the enemies except for one Nekomata, let her reach the highest level you can catch, then catch her. Revive at the hospital, use her to earn some more money if needed, then use her as your highest level character to catch an even higher level Nekomata.
Say your highest level character when you started the stage was level 15. You could catch a level 30 Neko; use her to catch a level 60 Neko; use that one to catch a level 124 Neko; use that one to catch a level 236-259 Neko; etc. You could eventually catch as many level 9999 Nekomata as you wanted. You could also use them to clear the stage of other level 9999 Nekomata and Beastmasters for enormous money and Mana. Having such high-level characters made power-leveling other characters much easier too.

Like I said though, this only worked on the PS2 version.