I suffering from bipolar disorder and the daily night shifts doesn't help my condition either. I want to be rolled-off in the project but I do not know how to say or start with this in a polite manner.
Politeness is about the words you chose, and your tone, and not so much about what you are asking for. Be clear about what you are asking for and why.
If you want to be taken off of a project, it's not going to happen if you don't ask. It also might not happen if you do ask, but if it's something you need for your well-being, than find a way to make it happen for yourself. You are worth it.
the daily night shifts doesn't help my condition
I think you mean that you have to work nights, and that working nights has been detrimental to your health in the past. (Even if it hasn't been detrimental yet in this job.)
So, we are really close to an employment law question and the two problems I have are that I don't know your jurisdiction... and I am not a lawyer (IANAL) :-)
Given that, I'll still suggest a few things:
If my assumptions above are correct, you can talk to your health professional about it and request a "doctor's note." It doesn't need to mention bi-polar, just that you request the "reasonable accommodation" of being moved to first or second shift.
The employer may not regard this as reasonable, especially if it was part of the offer they made to you. Or if it was part of the offer when it was made to your employer.
You can talk to your health professional about it and see if there are different drugs or dosing that will make it less likely that your bipolar will flare up during night work. In addition to IANAL, I'm also not a pharmacist, nor have I any medical training (except an old CPR course).
If the lack of daylight is an issue, maybe you can adjust to be awake more daylight hours. What I did in college: sleep from 2pm-10pm so you are rested for your job (Midnight-8 AM) but still get six hours of sunlight (from 8 AM - 2 PM).