Playing a melee class, if it is Dragoon or Monk, is going to take time learning what the boss does. Nothing much different then what everyone else here has posted for you mate. Most of the bosses, have a set rotation of abilities they will cycle through, in a set order. Learning these orders will be key for any melee. Even with a great connection, if you are new to the encounter, until you learn it will be rough on you.

Many people here already have pointed out things about your connection. Latency plays a big part in any online game. Battleping is my option of choice, but there are many different ones out there. I like the others, Battleping has a trial version that you can download and try out for free, just will DC you from game after 20 mins while using the trial.

The best fight I can suggest using something to test your latency, would be Titan HD. Seeing the plumes getting outside of them but still getting hit, to seeing them and dancing on the edge of a plume is a major difference. Works well the the trial of Battleping as well, since you have plenty of time to see the effect it has on your game.

So in my opinion, it is probably a little combination of both, learning mechanics of end game, and latency.