Is there a legendary biography of Avalokitesvara/Kwan-Yin/Chenrezig? I've googled this, but can't find it. I know there is a tradition of writing legendary/mythological/fictional biographies (hagiographies) of monks in the Chinese tradition.

Just a few days ago was the celebration of Kwan Yin's going forth day, but for the life of me, I can't find any other accounts of Kwan Yin's life as a monk or nun.
Also known as Chenrezig in the Tibetan tradition, Avalokiteśvara is widely known through most Buddhist traditions.

According to legend, Chenrezig made a a vow that he would not rest
until he had liberated all the beings in all the realms of suffering.
After working diligently at this task for a very long time, he looked
out and  realized the immense number of miserable beings yet to be
saved. Seeing this, he became despondent and his head split into
thousands of pieces. Amitabha Buddha put the pieces back together as a
body with very many arms and many heads, so that Chenrezig could work
with myriad beings all at the same time. Sometimes Chenrezig is
visualized with eleven heads, and a thousand arms fanned out around
him.

He has a total of 33 forms, including the wrathful form of Mahakala
He is also considered to be the &quot;parent&quot; of Tara

In Tibetan Buddhism, Tara came into existence from a single tear shed
by Avalokiteśvara. When the tear fell to the ground it created a lake,
and a lotus opening in the lake revealed Tara. In another version of
this story, Tara emerges from the heart of Avalokiteśvara. In either
version, it is Avalokiteśvara's outpouring of compassion which
manifests Tara as a being

He is mentioned in the following sutras :

Lotus Sutra
Kāraṇḍavyūhasūtra
Heart Sutra
Nīlakaṇṭha Dhāraṇī Sutra
Eleven-Faced Avalokitesvara Heart Dharani Sutra
Cundī Dhāraṇī Sūtra

Pictured below Avalokitesvara in his 1000 armed form and as Mahakala, and Tara