I dont know if the game was actually on the ps2, and I dont remember the games release date. I apologize for the confusion. I suggest the ps2 specifically because it was one of the consoles my cousin owned (I played the game at his house several times), along with an og xbox and a ps3.

The game was 3d, and had graphics similar to ninja gaiden 2, but with simple textures (hence the ps2 idea). The game featured dismemberment, like ninja gaiden 2. There were 4 playable characters: a skinny, decrepit looking old man with a spiked club (looked a bit like a short kanabo), a fat guy with a topknot and a very chinese looking polearm (like a guan dao), a young man with a katana, and a woman with dual swords (i think, not sure about her weapons).

Each character could unlock a second weapon and other equipment over the course of the game, but I never got far enough to find all of it. The old man could unlock dual blades that looked like karambits.

The first level let you play as either the old man or the fat guy. You started near a boat on a beach, and had to cut your way through enemies while making your way up the beach towards the mouth of a valley. For some reason, maybe due to the lighting, this level looked almost grayscale, all the colors were very desaturated. The second level let you play as the young man or the woman, and had you running through a walled city looking for an escape.

Ive posted about this game before, and some games that arent what im looking for are: Genji series, Jade empire, Shinobi, and Nightshade. Any further suggestions would be greatly appreciated. Thank you for your time.