The most efficient way to catch large volumes of Giant Mantis Shrimp is to wait for it to be Fish of the Day at Gokk'lok Shallows (Tangled Mantis Shrimp Cluster and Large Tangled Mantis Shrimp Cluster). Without an active Fish of the Day migration, the fastest method of catching Giant Mantis Shrimp is to travel round the coast of Pandaria fishing Giant Mantis Shrimp Swarm. Krasarang Wilds and The Jade Forest have the greatest number of these pools, although all zones with a lengthy coastline contain plenty of Giant Mantis Shrimp Swarms, except Townlong Steppes, which has very few.
In the aquarium hobby, Mantis Shrimp are made out to be the worst, monstrous creatures that have ever inhabited oceans or aquariums. For those marine aquarists that have lost many a valuable specimen to a Mantis Shrimp, you can see their point of view as to why they have this reputation. However, if a Mantis Shrimp is accidentally introducing into your tank while adding some new live rock, what do you expect from a carnivorous creature like this? Is it the shrimp's fault it ended up in your tank and began to eat everything in it? Mantis Shrimp may "seem" to be monsters, but they are just doing what they naturally do... hunt!
Mantis shrimp are among my favorite animals, and for good reason. Otherwise known as stomatopods, they diverged from other crustaceans over 400 million years ago during the Cambrian period, so they are only distantly related to the likes of shrimp and lobsters. Many are very brightly colored, like the one above. Some are also fluorescent.
There are ~350 species of mantis shrimp (Stomatopoda). Pictured above is Odontodactylus scyllarus (source: Patek & Caldwell, 2005). They are easily recognisable in the field by their colour and appearance, but more scientifically by their flat carapace that leaves the sides of the thorax exposed and doesn’t even cover the last four thoracic segments. Thoracopods 2-5 are subchelate (claw-like), especially the second thoracopod which is transformed into a proper raptorial appendage reminiscent of a praying mantis’s (hence the common name). They walk on their 6th to 8th thoracopods, and if all else fails, you’ll also recognise them from their huge eyes on moveable stalks.