What does “have the avocados” for anchorman work mean?

Solution 1:

The phrase is a humorous, off-the-cuff euphemism for testes, and thus metaphorically implying grit, determination, boldness, toughness, and other testosterone-associated qualities. The historical connection between avocados and testicles is probably not relevant (except to the extent in which the shape and texture of an avocado makes it a natural testicle substitute).

Nearly any object of the right size and shape can be called into service as a one-off testicle-euphemism, with rocks and stones being typical, and balls being so often used that they can't even be considered a euphemism any more. In regards to the original example, the fact that avocado is not in common use is deliberate --for comic effect.