Wonderful question! I guess it depends on how you define ‘win’. Seagulls have the ability fly (which walruses don’t), and can also handle themselves underwater (they’re very adept at spotting fish below the waves, diving in and grabbing them).
However, walruses are rather large creatures, with very, very powerful jaws. It’s almost certainly possible for a walrus to eat a seagull in a single bite. They’re surprisingly agile (in the water, at least), very strong, well armoured (that’s what all the blubber is about — insulation and padding) with thick skins (metaphorically and literally!).
I think that things don’t look good for the seagull here: it’s a one-bite post-lunch snack for an angry, hungry walrus, and it’s moreover fundamentally very unlikely to be able to actually hurt the walrus. The best the seagull could hope to achieve is a speedy, effective retreat.
I think it depends on the precise situation of the fight. Naturally, both of them would retreat as soon as possible, because they have nothing to gain from fighting, but let’s supposed they were hypnotised to keep fighting and not to retreat.
I think the seagull would win. Seagulls are great at swooping down and pecking at things, and they’re pretty big and powerful when they do so, and really agile. I know people who have had icecreams taken right out of their hands by nifty seagulls. If they’re too agile for a human, a walrus has no chance.
The seagull could keep swooping down and pecking at the walrus. The poor walrus wouldn’t be able to get a hit in, particularly if the seagull pecks at it in the right place. It would just be too agile for the walrus to get a bite in.
Eventually the walrus would die from blood-loss, or get it’s organs damaged from too much pecking. It would take a while.
Moral of the story: *Never* mess with seagulls, even if you’re a walrus.