How can I stop someone from hurting me when they don't care about my feelings?

If someone is repeatedly hurting you and disregarding your feelings, then if you are able you should cease contact with them. That is the only way it will stop.

Sometimes, when we feel like someone doesn't care about them hurting our feelings, we have to bite the bullet at some point and let go as letting go can be a lot less painful in the long run. Although it may seem crazy, like where we will feel hurt letting go. It's better to go through a period of time feeling hurt and in pain for letting them go, than to be continuously going through it throughout your life.

Look in their eyes and say 'nothing you say and do can hurt me' it doesn't necessarily change the other persons mind to hurt your feelings but what it does is give you a strength in the back of your mind, that you are strong and whatever the other person says is nothing but rubbish

By setting strong boundaries, yet still respecting other people's feelings and emotions as I would want them to respect me

It depends on the situation. Generally, I do my best to walk away. If I will be required to see this person often, I will address it directly as I'm responsible for how I allow others to treat me.

The answer is found in your question. "How can I stop someone from hurting me...". That's just it, you have all of the power. People can only hurt you if you allow them. Focus on what you can control and let go of what you cannot control. Otherwise, you'll be on a never-ending endeavor that will leave you mentally and emotionally drained. Love yourself and others will see that and resonate with them. Therefore, do what makes you happy and that is all that will matter. If the other person doesn't care there isn't much you can do, so let it be. I hope this helps you!