I have Staghorn's & have never seen anything like that, do you have it indoors or out? Just a wild guess but wonder if it's too wet?
Mine are mounted on a pieces of wood hanging outside under my patio & do great there, I got my original one at a garage sale & it was already mounted, I've mounted some of the babies myself. I bring them in if there's a threat of a freeze in winter but put them right back out soon as it warms up, usually never more than a day or two. I water them freely - any not needed drains right out.
I read on one of the forums a while back that banana peels are good for them, gave mine some & they perked up so I cut a ripe banana in half shared it with two of them & they really liked that too.
Sorry I don't have any suggestions for the black spot, hope someone else will...:-)
Good luck

staghorns do better if they are hung on wood. my guess is that your fern is too wet and may be rotting. maybe it is getting too much light? they like semishady areas that are at room temperature.

All that 'banana peel is good for them' stuff is nonsense - the kind of chinese whisper that gets internet gardening lore a (deservedly) bad name. Ferns want nitrogenous nutrient, NOT phosphates...and Australasian ferns in particular. Fortunately, banana skins are so useless in all the nutrient categories that you are unlikely to do any harm (unless you concentrate the phosphate content via worm-compost liquour, say) but bananas are the opposite of what your ferns require.

Seaweed extract is the safe organic route to delivering nitrates to ferns, while keeping the P and K proportionately low.

Steve - Brighton, UK

Mine is hanging on my screened in porch. A friend told it looks like black-spot (fungus) and to use a mixture of 1teas. peroxide to 1c. water and spray it. I did that, and so far so good.

Steve...I have a small amount of worm castings in the basket. I was told by a Nursery owner here (who has a HUGE staghorn) to use a small amount of potting mix. My potting mix is mixed with worm castings. Could this be a problem?