hfinney
I'm not the best at this, but I'll give it a try.
It looks like a male red- or orange-headed, blue-backed, white-breasted gouldian. At first I thought it was seagreen-backed, but the seagreen birds had red heads, rather than salmon-colored heads in the images I saw. (On a semi-related note, I'm not sure exactly what seagreen-backed gouldians are. Maybe mosaics? Though I don't know how that works.)
Red-head is dominant, so it would only need one allele for a red head. Orange-head requires the bird to be genetically red-headed with two recessive alleles on another gene that also affects head color. However, red-head and orange-head look the same in bluebacks, so that bird is most likely red-headed, as dominant traits are easier to obtain.
White-breast is recessive to lilac-breast, which is recessive to purple-breast, so it would have to have two alleles for breast color.
Blue body requires the bird to be genetically green-backed with two recessive blue alleles on a separate gene that also affects body color. It's a bit like orange-head in that it is dependent on two genes. This bird has two green alleles on its body color gene on its two Z sex chromosomes; if it had a yellow allele as well as a green allele, it would be pastel, and the blue color would be faded. This would not occur with a female bird, as they only have one Z sex chromosome, and therefore could only have one allele for base color (green or yellow). This is why only males can be dilute, having both a yellow and green allele.
(Well, today I learned body color inheritance; at first I thought blue was recessive to yellow which was recessive to green on the same autosomal gene, but I guess not.)
All in all, this bird would be difficult to get through breeding, and the combination of traits is probably rare.
Here are some useful articles on mutations:
Gouldian Genetics
Body Colors