She's first 'seen' on the news; technically, there was news on the television that something had capsized a G.U.N battleship, and Tiamat was later found out to be responsible for it (after telling Tina the Bat so).
Sephtis, White, Tina, Calvin, and Micah end up encountering her after heading out towards the Northern Great Sea, and White ends up getting into a fight with her as well, using electricity to keep her at bay. After an unaffiliated aircraft shows up to help White and the others, Tiamat gets into a fight with that, and manages to severely damage it with an icicle spray from her mouth.
The squadron from the aircraft manages to rescue Calvin and Micah, and Tiaamt, thinking she'll finally have peace, goes back below the waves, only to get electrocuted by White again; him, Sephtis, and Tina had ended up staying behind, and this unsurprisingly makes the dragon furious, attacking the trio with a blast of Nitrogen.
Although Sephtis and White seem to want to kill Tiamat, Tina attempts to reason with the ancient beast, asking her why she attacked the G.U.N battleship. Tiamat tells her that they were in her territory, and that she "knows their type", claiming that they wreak havoc upon the land and destroy everything that seems even the least bit 'monstrous' to them. It is possible that she believed G.U.N was attempting to hunt her down, and she acted in self-defense.
Later, Dr. Eggman arrived at the ocean with Razer - being used as Eggman's weapon - bound within the core inside the Egg Carrier Mk. III, and firing off a few rounds as to get Tiamat's attention. And despite the trio doing their best to stop Eggman from capturing Tiamat, they were unsuccessful in doing so, as Eggman fired off one, massive shot at Tiamat, which results in a direct hit and being extracted into the base by the tractor beam.