Which is correct?
a) [doing something] for all its worth
b) [doing something] for all it's worth
Both can be justified. In (a), you are doing something to the extent of its value; the construction can be likened to "going for the gusto". Though perhaps there you have the prepositional phrase acting in the place of a direct object, which it isn't really in (a). (b) expands to "for all that it is worth" which essentially means the same thing as (a). So from that point of view both would be correct - but one had to have been the original phrasing. I wonder which?