I don't know how accurate this is, but here's one interpretation:
By Melanie Jones, published 20th June 2010
This ‘rainbow portrait' of Elizabeth is riddled with symbols:
One not so subtle is the eyes and ear embroidered into her dress, probably a symbol that she sees and hears all. Who could doubt that with all the rebellions, plots and conspiracies she had survived?
Elizabeth is being shown as wise, as her sleeve possesses the most cunning creature, the snake.
She is also dripping with jewels and fine fabric, depicting her majesty, splendour and wealth.
The beautiful crown on her head is a symbol of the monarchy. Her portraits have long since passed the time when they needed to show she was the rightful queen; Elizabeth is the monarch.
She is also wearing pearls, a symbol of virginity.
In her hand she holds a rainbow, a symbol of peace; she possesses peace.
Another common symbol of monarchy (and indeed life) is the symbol of the sun. Without the sun, there can be no rainbow, and since Elizabeth holds the rainbow, what else can be concluded except that she is the sun (the Latin inscription implies as much) Elizabeth is the sun, and the crown.