How do you deal with the embarrassment?

What are you embarrassed about?
the fact that you have an aging parent that needs help?
if your parent has dementia and they do things that "embarrass" you?
Were your parents "embarrassed" when you threw a temper tantrum in the store because you wanted a candy bar? or when you wet your pants on the playground because you couldn't get to the bathroom in time? or when you made a comment about the way that person in front of you dressed or walked?

If you want better answers detail your profile a bit better or edit your post to include more detail.
If this is about dementia all I can say is the journey does not get easier, the declines get more difficult to handle. If you are not prepared to do this begin looking for a facility that will be able to handle the care that will be necessary. This does not mean you "give up" it means that you are acknowledging that you can not do this at home. There is help, there are ways. From hiring caregivers, finding Adult Day programs to full time care in a facility.
If your parent is a Veteran the VA may be of help.
Contacting your local Senior Center and asking what help is available is a good start.
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There is no such thing as “embarrassment” when dealing with taking care of someone with dementia. The best reaction is compassion and understanding.

Anyone who criticizes you or the LO YOU CARE FOR is not worth of your time or consideration.

What are you embarrassed about? You'll have to be more specific if you want any answers.