Hans Holbein the Younger was born in Augsburg, Bavaria in 1497. His father, Hans Holbein the Elder was also a painter and raises the question — Was there a third Hans Holbein, and was he known as Hans Holbein the Even Younger Yet?
Hans traveled to Switzerland and became a friend of the Dutch humanist Erasmus, who asked him to illustrate one of his books. Hans also illustrated Martin Luther's German Bible translation. Because of the unrest caused by the Reformation, Hans went to London where he met Sir Thomas More. It was during this trip that he painted A Lady with a Squirrel and a Starling. (He returned to England later on and became the court painter for King Henry VIII.)
The lady in the painting is thought to be one Anne Lovell — because squirrels were featured on the Lovell family coat of arms and because the Lovells owned a house in East Harling, in Norfolk, England. (Harling/starling is somewhat of a reach, but at least he didn't paint her hurling.) But on the other hand, Holbein painted animals into many of his portraits, so nobody knows for sure. It's pretty certain that the woman didn't pose with the animals. They were painted in later. At least one reviewer thinks the hands look masculine and belong to an assistant that posed later.
The pose, with the woman impassively looking away from the viewer, is typical of Holbein's work at this time. The notable feature of the piece, however, is the skillful painting of so many different textures — the fur on the cap, the cloth on the shawl, the cambric at her throat, the feathers of the starling, the fur of the squirrel.
I'm also told to notice the way the curl of the squirrel's tail mirrors the curl of the plant in the background, but I'm not learned enough at this point to understand why that's notable. Does it have something to do with curling?