The obvious answer to "What genre is Tristram Shandy" is "Autobiography." It is, after all, called The Life and Opinions of Tristram Shandy, Gentleman.
Wouldn't it be nice to have it be that simple? The problem is, as we've talked about, that Tristram Shandy has hardly any Tristram Shandy in it. It's got dirt on just about everyone except our beloved hero.
So maybe it's just a big satire? Tristram is one crazy comedian, laying into sermons, ancient writers, soldiers, love affairs, philosophers, theologians, women, London, landowners, writers, critics, and readers. He parodies one writer after another, sometimes so subtly that you'd have a hard time figuring out what he's going after without a really good set of annotations.
Then again, Tristram Shandy gets philosophical in no time flat—even though it's a weird brand of Shandean philosophy. Shandyism is an attitude toward life exemplified by "a careless kind of a civil, nonsensical, good-humoured Shandean book" (6.17.8). The digressions, dirty jokes, and sentimentality are all part of a philosophy of life that Tristram is trying to get across. So the book does turn out to be The Life and Opinions of Tristram Shandy, just much more roundabout than it seems. Leave it to Tristram to make up his own genre.