I can't remember the name of the game for the life of me but I remember a game where you had to fight through a random number of enemies on each floor/level of a tower and you had to try to reach the boss at the top. If you died, you had to start back at the bottom. Does anyone remember the name of this game?
Any more specifics? Style of gameplay, i.e. twin stick shooter, RPG, etc? Remember any specific characters?
let's try the "teach a man to fish" approach... here's what you do: go to https://www.mobygames.com/browse/games/psp/ and start narrowing things down by picking a genre, theme etc, whatever you remember. then go through what's left and look at the screenshots.
This is a very great PSP database here: http://www.advanscene.com/html/dbpsplst.php you might be able to find your game there
Do you at least remember what the graphics looked like? Was it released in USA/Europe? There are a few games that fit the bill but can vary by gfx or if it was localized. =)
There was a ps2 game based on the same concept, from atlus I think... name slips mange but was a Saturn exclusive for ages