I made a movie of the first stage, but unfortunately it went out of sync because Arthur didn't jump like he was supposed to at one place, so I wont post it.
Anyway, jumping is a tad bit faster than running along the ground, so constant jumping will help, also you can throw stuff in 4 directions while jumping without any pause, which means that you should never have to stop unless you're forced by something like a guillotine. (I was forced to stop at one, but only for like 10 frames)
I'll see if I can fix the first stage I played, then I'll post the movie, you can use it as a kind of "guide" or something like that.
Edit:
http://files.upl.silentwhisper.net/upload5/Ghouls_--N_Ghosts_-REV_01-_-JUE-_---.rar
I hope the persons who wants to see this can open .rar files, anyway it's definetely improvable, and you could also kill more to gain more points, getting another weapon from the chest I wait at may also speed things up later in the game, I don't know.