Briefly, a couple years ago, I attempted to get the Rainbow Portrait; however, I failed to realize that it wasn’t a legendary drop and I didn’t learn of this until after a couple hundred runs, which means I might’ve missed it.
Can said bear spawn more than once?
Absolutely. It’s just a huge RNG roll whether or not he appears in game. He can appear any time you run the level.
Get back to farming!
What is his spawn rate? Is it worse than Princess Lillian?
Yeap. I have it spawn 2 runs in the row while seeking frame and sword.
No. Nothing is worse than that.
The chance of getting Wirt’s Original Leg is worse than Cosmic Wings. The former has three layers of RNG, the latter only has two.
Number of layers doesn’t show nothing. The probability on the each layer do.
I got my Cosmic Wings long ago–at the time I didn’t even realize how rare they are. I’ve been after the Rainbow portrait for years–I craft a Staff of Herding every season, and since the inception of the Altar, I craft two of 'em. Every time I start a new game, first order of bidness is go hunting for that little teddy bear barstard. No joy–have yet to even find the little #$%@&* ! 
Bluddshed said he got his Portrait on the first run! I haven’t kept track, but I’m, somewhere, in the low hundreds of runs.
He now works for Blizzard.
Over 500 runs this season, and probably 100 before. Absolutely nothing. Starting to wonder if it was removed from this season :\
If you also farm Sir William in EU, do not hesitate to send me an invite: I will be farming him next season in multiplayer.
Unfortunately, I’m strictly NA, but thanks for the offer.
J
Don’t give up. I finally got it this season.