I've heard of bipolar cases where the applicants were granted skilled immigrant visas. However, I would suggest that you have a plan to help manage your condition once you get here. Not so much in terms of medication, since that is available here, but in terms of triggers. The transition is not always easy and there will be a lot of adjustments. I know of two cases where all the changes and difficulties that came with migrating became too overwhelming and one person ended up going back home for over a year, while another was unable to work and was under medication for quite a while.
This is not to discourage you or to scare you. It's just to let you know that yes you can get the visa, but you really need to prepare yourself and ensure you have a support system in place when you move.