Left Foreleg

After you complete the sevel Missions given by the circle of Cie'th stones in the Eastern Tors, most of the Adamantoises on The Archylte Steppe will become Long Guis. These are much tougher versions of their brethren, and are notably immune to Death, so cheap tactics won't be as effective. Once again, summoning will immediately disable the beast's legs. Their Physical and Magic resistance remain high, but their Chain Resistance drops to 10 and they become vulnerable to everything except Pain, Fog, Daze, and Death. Poison is very effective, as is the combination of Imperil and En-spells, and obviously Deprotect and Deshell are vital. You'll most likely have to disable their legs at least twice to achieve victory, though, so you'll either have to use an Elixir or be able to legitimately take out the Long Gui's legs.

Fighting the Long Gui while standing is difficult, as their normal attack is devastating, and almost everything else they do (such as Ultima) basically requires you to immediately switch to the Tortoise paradigm (SEN/SEN/SEN) to survive.