I can't trust my supervisor anymore, but have to have his letter of recommendation. What should I do?
If you submit an application with a bad reference, it will quite probably sink your application. On the other hand, simply ignoring the requirement in the application may lead to a desk reject. 

However, if obtaining a good reference from your advisor is not going to happen, you should probably address that up front in your statement of purpose and include the reference anyway. Disclose, in a neutral fashion, that you had difficulties with your previous supervisor, and focus on what you learned from that. If you can show in your SoP that you can endure challenging situations, and even grow from them, while also showing you are able to conduct high quality research, this may outweigh not having the critical reference.

Pros:


It meets the requirements of the application (if, indeed, you have verified that this is a hard requirement)
It demonstrates that you can endure challenges in research, as you will inevitably face more during your PhD (just hopefully of a different nature)
It shows maturity in your application (by favouring openness and transparency)


Cons:


It includes a weak reference letter in your application, if you can even persuade your advisor to write it
It risks presenting (rather than concealing) less savoury characteristics of your past research profile, which shows that you're not a "golden," flawless candidate.