Lace 1's parry only activates if you hit her from the direction she's facing.
Does not work against Phantom or Lace 2
In later patches, she will continue to parry you while attacking if you slash too close to her (same with Lace 2)
1scripted first phase w/ parry and a setup(in the first vid) to start 2nd and 3rd phases w/ a parry, as soon as you see the cog dancer move slash and parry. for the last phase you have to slash twice since they are slower.
first video is w/ damage tank scream skip, second video is w/ parry scream "skip", parry scream skip is slower but you dont get hit so its safer.
the timing is slash parry right after the cog dancer hits the floor, dont rush it, its fairly easy to do it too early.
in both you could def do a parry to end the first phase sooner but then you wouldnt be able to start the second phase w/ one, im not sure which option is better but know that reacting to the first attack of the second phase is pretty hard if you start w/ a parry.
also tip for practice, debug has a bind that doubles the game's speed while held, for me its right shift but i dont rember if i changed it, its pretty useful for the big waits in the middle