The reason Milarepa is the most beloved Tibetan Saint is that he did bad things and over came them and so redeemed himself which gives hope to all Tibetans and people around the world.
Almost everyone accidentally or on purpose does some bad things as a younger person and then has to try to (make it right) as they become more mature adults. So, Milarepa's story touches us all in this way.
As a young man in I believe around 1100 AD, Milarepa was the son of a very rich Tibetan family. When Milarepa's father died he left his wealth in the hands of his brother. But, his brother instead of taking care of Milarepa and his mother and sister, enslaved them and made them his slaves. This really pissed off Milarepa's mother to the point where she sent Milarepa to a Sorcerer to learn how to kill his Uncle and Aunt and their family. So, this is what Milarepa did. He created a hail storm at a wedding which killed his aunt and uncle and their whole family. But then, Milarepa felt remorse at having done this for his mother and then went to study with Marpa, the Translator and over the next 50 years of meditating in Tibetan Caves became completely enlightened to the point where he could heal people, fly, and other Siddhis and empowerments. He sang people to enlightenment through his songs as well. People would come to him in his cave retreats and his skin would be green often from eating only nettles to live and he would teach them how to be enlightened fully.
So, in this way he became Tibet's most beloved Saint. Marpa and Milarepa are the foundation of the Kagyu lineage of Tibetan Buddhism. The first to arrive was Nyingma from Padmasambhava, the 2nd was Kagyu through Marpa the Translator and Mila Repa. Also later arrived the Sakyas and the Gelukpas. The Dalai Lama is Gelukpa and is considered the head of all Tibetan buddhist lineages since around the 1500s or 1600s. Padmasambhava first brought Buddhism to Tibet in the 700s or 800s AD from the famous Buddhist University of that time called Nalanda University in Bihar province near Bodhgaya where Buddha became enlightened under the Bodhi tree.