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Based on some screwing around and observations of my own playing style I think I have an idea as to how to unlock the skills. I think that it's very similar to the "Jump 100 times" art unlock thing. I have a tendency to cut my enemies down on the ground whilst running and the first unlocks I got were the 3 hit combo. After I got to the final boss I decided I wanted the half cost ability so I went running about the net trying to figure out why I'd only unlocked half of the skills.
The two walkthroughs here weren't much help, but one mentioned that they'd found that the fastest way to unlock the half cost skill was to run through the first level spamming the level 1 lightning spell. After trying it I noticed that it killed a minimum of 3 people per shot. So, for the fun of it, tried killing as many people as I could with mid-air slashes. Guess what I unlocked after 1 play through the level. Mist Blade.
Megaman Zero series implemented a similar system of unlocking abilities so it's no big surprise to see it again, but, unlike the Zero series, TLK2 doesn't lead you through the steps and it will take some time to figure out exactly how many times you have to kill someone with that technique.
I noticed that I leveled up bodysplit sometimes when I didn't even use it, so I think that this one is linked to your playtime, since one of the times it leveled was when I my playtime was 6 hours, the next I think was 8 or 9 hours, and on both those missions I didn't use bodysplit.