Half Pendant of Aquatic Endurance

This item plays a large part in the druid quest Trial of the Sea Lion, part of the Aquatic Form quest chain.

When combined with the Half Pendant of Aquatic Agility, this creates the Pendant of the Sea Lion.

Source
This pendant represents the ability to remain underwater indefinitely. For both Tauren and Night Elves, you have to dive deeply for this, usually past the 'point of no return'. Fortunately, there are bubble fissures nearby where you can catch a full breath before continuing.

This item is found in different places for Night Elf druid than it is for Tauren druids. Clues to its location are given by the druids in Nighthaven, Moonglade.

Alliance: Longshore
Swim out into the ocean from due west of Gold Coast Quarry. Head north a bit, and look down as you swim. Shortly before the ocean floor drops off into the depths (and the minimap displays a different color for the water), you should find a LARGE anchor. Swim down towards it and aim more west. You should see a bubbly fissure, with a Strange Lockbox nearby. The pendant half is in the box.

If you swim over the bubbly fissure, your breath bar will be filled up.

There are a few elite sharks among the sharks in the area before the drop-off. The wary can easily avoid them.

You will also note a shipwreck in water only a little ways further out from this point. You CAN reach it and swim around it, but it is in the deep Great Sea and you will be fatigued. While it may be novel to you, there's not really a lot to see there. Don't get caught short of breath OR endurance.

Horde can also get this one too 18, 33

Horde: Silverpine Forest
North of The Sepulcher is a beach with a large wreck on it. Head straight west from the wreck on the beach until you hit the drop-off (right about when you hit the "Great Sea" zone). Down at the bottom is a fissure where you can breathe, next to the fissure is the chest with the pendant half. You won't see the fissure/chest from the surface, so ... have faith. And hope.