Strategy For Victory
Once you've completed Mission 02 - Goodwill Hunting, the Cie'th Stone for this mission will become active. After accepting the mission, the Ugallu's location (as always) will be represented by a pink star on the main map. Follow in the direction of the star to meet up with your enemy and begin the battle.
Now I know this thing looks tough, and without the proper strategy, it is. But we shouldn't have to worry about any of that, because I just so happen to have the proper strategy to defeat this bad boy burnt into my memory. The Ugallu is alone, much like the Ectopudding in Mission 01, so this battle will probably be easier than the last one where you had to deal with quite a few different enemies at the same time. The Ugallu's stagger rate is actually very low, so your main goal in the beginning is to stagger him as soon as possible. Do this by using a Delta Attack/Mystic Tower Paradigm combination, switching back and forth from the two whenever you see fit. Once your enemy is staggered, immediately switch over to an offensive Paradigm, such as Aggression (Commando + Commando + Ravager).
After repeating this process a couple of times, the Ugallu should be history without much effort. One warning though, the Ugallu is capable of inflicting Poison and Curse, so be prepared to remove those two status effects at anytime during the battle, even if it means switching your Paradigm just as he's about to be staggered. You don't want any of your characters to get too low on health at any one time, otherwise there could be dire consequences. Once you've defeated the Ugallu, you'll receive three Bomb Cores. Oh joy, what a sufficient prize this is. Equip it to your resident Sentinel immediately.