Looking at the Story arcs and the Balam Alliance and looking at the purpose behind the batman trilogy films referring to the concepts of Fear, Chaos, Pain.
1. Fear: In the Batman Begins, Bruce is on his journey to find himself after his parents deaths because of his fear, and when he does, he fights to conquer his fear and turns fear against his enemies. Scarecrow and Ra's Al Ghul plan plunge Gotham into chaos by filling them with fear, Batman fights them by fighting his fears to protect the people close to him.
In Fairy Tail, Tenrou Island Arc, Natsu fights Gildarts and when Gildarts releases his power, Natsu fell pray to fear and Gildarts told Natsu that "Fear is not evil, it tells us our weaknesses, once we know it then we can become stronger and kinder." Grimoire Heart Attacks and they displayed their powers and caused great fear in the unprepared Fairy Tail mages. Once again at the final battle with Hades, Natsu and his comrades fall pray to fear, and Natsu rallies his friends and gives them courage because his conquered his fear when he has something to protect.
2. Chaos: In the Dark Knight, Bruce having saving the day countless times, but he soon finds that his skills are put to the test with the chaotic Joker. In his studies, the Joker is a supposed nihilist who believes in nothing, cares for nothing, and pursues nothing. He is a dog who chases cars, but doesn't know what to do when he caught it, so he just does things out of randomness.
In Fairy Tail, Oracion Seis Arc, Natsu and the rest of the Alliance fights to stop the Oracion Seis from getting their hands on Nirvana, and magic capable of switching light from darkness and vice versa. In final hours of Oracion Seis, the Six Generals falls and Zero rises, He who loves destruction and bringing nothingness, when Nirvana was heading towards Wendy's former guild Cait Shelter, when that was Brain's target, Zero says that it's meaningless, he has no reason to just destroy that but wishes to destroy everything and shall start with Cait Shelter, Zero in a sense is also a nihilist and brings chaos to the world.
3. Pain: In the Dark Knight Rises: Years since batman's disappearance from the public, Bruce tries to live a normal life, but his will have to wait when the mercenary called Bane comes to Gotham in hopes to destroy it and fulfill Ra's Al Ghul's destiny. Batman finally returned but only to be captured by Bane, and Bane plans to spiritually torture him by making him watch as he tortures his home city before destroying it, and when he does that he will allow Batman to die. That is the symbol of pain.
In Fairy Tail, Mashima hasn't given anything about Tartaros yet but if my theory/coincidence is correct, then the Tartaros will represent pain, they will probably force spiritual/physical/emotional/psyhological pain on Fairy Tail when they continue to fail to protect their comrades, family or people close to them, before destroying Fairy Tail completely, they will break Natsu and the others.
Please post for Ideas and comments.