UG Research Advisor Not Willing to Write LOR to support my transfer application. How to proceed?
It is fine to mention your undergraduate work. You did it and you received graded credit for it. Talk about it! (In a statement of purpose or something). 


What did you do?
What did you learn?
How did it inspire you?


True, yes, your undergraduate advisor would not write you a letter of recommendation. There is no need to mention that. If you have other people who are willing to write you a strong letter, you should be fine. When I sit on admissions committees, there are a few things we take into account:


We are only seeing a portion of the student's profile. We don't know the whole story (either way). 
Sometimes professors are hard to get along with in regards to grades, authorship, LORs, etc.
Students are going to school while life happens around them. This means that sometimes the circumstances of life will affect their decisions and opportunities relative to school.
We do not expect a masters student to come in on day one and have the skill set of a master's student at the end of his or her degree. We are looking for potential.


Overall, I am more interested in learning about what you, not an advisor, did. If you are competent in explaining your research, that is going to bode better for you than having a LOR from someone who grudgingly has been forced into writing you a LOR.  I would not spend too much time trying to make this donkey (the undergrad advisor) pull the cart (LOR) he does not want to pull.