a few ideas I got:
have you tried attacking when doing the UP+UP+CROSS jump? I think attacking makes the jump a bit longer (may be faster for 1st level and others), or you could try doing the double jump but it doesn’t always work
1st level: are you sure it’s faster to use the hook ASAP at the start of the level? at the start, the camera isn’t focused forward, and the hook is shot in the direction of the camera, so maybe if you walked forward a little until the camera is in place and then used the hook it could be faster
2nd level: have you tried starting the level with the hook? I was able to hook the furthermost roof by just pressing TRIANGLE at the start with no additional input, but when I flew I didn’t actually reach that roof but the one before, which makes it slower; but if it’s possible to reach the furthermost roof then it would be faster (I’m pretty sure, I made a comparison with videos)
3rd level:
video of a different strategy, maybe it’s faster?
and I have a question: how did you make those movements at the end of the level 6 boss fight? O_o you did the CIRCLE+CROSS move and attacked while doing it, and after you threw the shuriken you made a weird jump