No, really.

A fluffy toy bear, that is. Two feet high, two feet wide :-) with
fully synthetic fluffy fur that used to be white and now has
accumulated dust and general grubbyness after sitting on top of a
cupboard for years.

I can't think of a way to clean something like this except to treat it
a bit like a three-dimensional carpet cleaning job, hence the sponge
bath idea.

Yes, I checked for care labels. None present, and even if there were
it's too big for a washing machine. So, what IS the best way to
approach this daunting task ?

Any hints appreciated.