Wiktionary is the only dictionary I found that lists
titsup as a single word, describing it as merely an alternative spelling of the two word version
tits up.
There's quite an extensive discussion of the origin of
tits up here. The acronym as ultimate origin seems dubious. My guess would be that the two-word expression came first, possibly derived simply from the idea of a dead body being flat on its back: "belly up", "toes turned up", etc. Later on, a backronym was coined, and subsequently the expression was sometimes written as a single word, to match the supposed acronymic origin.
The News on the Web corpus has 59 examples of the single word spelling, some in lower case and some in all capitals, but 58 of them are from the Register, the same website that TRex linked to. The only example not from the Register was from a reader's comment on a UK football fans' website. The iWeb corpus has 32 occurrences of
titsup, 24 of them from the Register. The other 8 are almost all from readers' comments on sites covering either computing or football.
I'm not convinced we should allow
titsup. It seems to be an eccentric way of writing the colloquial expression
tits up, used mainly in one publication.