Sorry to hear this has happened to you.
Unfortunately, there is little recourse or protection available. Sometimes, there are legitimate reasons not to provide good recommendations, and in some cases, willing to have you, "a bad student", in their lab, would be legitimately more acceptable for them than putting at stake their reputation.
That said, for the admissions committee your inability to reconcile with your own MSc advisor is certainly a negative trait. I would only resort to that if you could not possible convince your advisor to provide you with a good LoR. If the situation is as you describe and your advisor appeared to be happy throughout your MSc program but now is making an U-turn, you have to communicate clearly that you are not planning nor willing to do a PhD with them. If, instead, they were nagging you to work harder the entire time and you believe that the project has turned out to be good, well, is it what it is, the advisor simply would not write you a good LoR because they do not believe in it.
If you ultimately decide to get LoRs from someone else, that is possible, but the question about your advisor's opinion about you is imminent still. As a measure of damage control here, you could try putting more emphasis on your thesis. Their review of the thesis as submitted to the thesis committee (if this practice is used at your home university) could be supplied as evidence that they do not think as poorly of it as they communicate during admissions, but it is quite a stretch, especially given you do not seem to be a native English speaker and said review would presumably require translation.
All in all,
- Try to convince your supervisor to provide you with a more positive LoR. If the entire issue is, indeed, them expecting to make you work in the lab for a few more years as a PhD student, you could just claim it would not be happening.
- If (1) is not possible/feasible, do it without providing a letter from your supervisor, but prepare for a lot of struggle. It will be an uphill battle.