Brown Glob

Tripod.com says that

In the mid-1950s, a diver, while watching a shark, saw a big, brown shapeless thing  head over towards the shark. The shark convulsed, and then didn't even try to escape as the thing came and grabbed the shark. Chances are that a large jellyfish would best fit the description.

The same webpage offers evidence that may explain the sighting as of a lion's mane jellyfish:

In 1973, the ship, Kuranda, collided with a gigantic jellyfish while sailing to the Fiji Islands. One seaman who was hit by the jellyfish's stinging tentacles came away with severely burned skin (he died from the injury). The jellyfish also started to push the ship down with it's [sic] weight. An SOS resulted in help from the Hercules. The crew of the Hercules managed to get the jellyfish off the ship with a high pressure hose. Later, when the slime from the jellyfish was analyzed it turned out to be from a species called lion's mane.

It is not clear where the diver saw the brown glob, however, and jellyfish are not known to prey on sharks.  This could then be an entirely new genus, or an unknown type of jellyfish that is more predatory than its brainlessness would make one guess.

http://www.aquabeasties.com/2010/03/if-you-think-legendary-sea-monsters-are.html

Sources:
Tripod.com - kodos86