This is a boss fight when you make it to the end of the the camp falcon bats stage in the asylum.
You will have encountered some little girls a few minutes earlier who only appeared in another "world" and as such who you could only see to kill half the time.
This boss fight follows similar lines in that you cannot see the Lady except when it goes dark and then only for a few seconds to get some hits in.
The plus here is that her health bar is very small compared with the other bosses. What I did was move slowly so she would catch up to me and use my Chi as soon as it became dark to get some hits in, the run/jump around til it recharged and then move slowly so she caught up to me and rinse and repeat. The toxic Chi also works well as you continue to see the hits on her when it goes light so you can continue to hit her in the light. Using this method it only took about 2-3 minutes and I only got hit once.
Hope this helps and good luck!