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I have been working on this for a few hours, easily the longest I've had to in this game's skill points (thanks to the tricks you all have discovered). I was trying and trying at this one and I read up on some of the frustrations and even giving ups on this. I think they might have tinkered with the PS2 version of this game a bit in such a way that it's not as easy to get as in the PSP version, my thoughts anyway.
Anyway, after some trial and error, I finally got it. What I did was that I reloaded the level by reloading the game and then playing through WITHOUT DYING. Once all of the enemies were dead, I went ALL the way back to the ship (this part is important). I was not able to do this earlier because for some reason, if I died after the door that leads to the lava hypershot area, I would not be able to go through that same door. Thus, I thought I just had to start from this door the entire time, since I could never go back for some reason. Anyway, if you don't die, then you CAN go back through this door, and I believe that is a significant part of it, as the "skill point timer" probably doesn't start or reset until you reach your ship. Thus, with all the enemies dead, I was able to just speedily make my way to the red button (I didn't get the skill point until I went through the door the button opens, btw) and I got the skill point.
I was honestly surprised, I thought this skill point was just bugged not to work at all on PS2.