|Unlike other bosses, you do not attack Bardam. He uses certain attacks in a certain order over three waves. If you get hit twice, you're out of commission for that wave. If all three players are knocked at at any time, you lose. If any one player makes it through all three waves, you win. Also, if you're looking in the battle log, Travail is the move Bardam uses to start off each attack round.
The first wave will begin with him summoning a Hunter of Bardam that first uses Magnetism to draw you to the middle and do two AoEs one to the middle and one to the outer ring., and then Empty Gaze which is a simple "look away" attack. Simple stand in the outer ring right near the break, and after the first AoE goes off move to the middle and then turn away from the Hunter of Bardam. Bardam's next attack will see several Throwing Spears line up along the edge and Charge across to form a grid with some safe spaces. This will strike several times, alternating which row and column they cover. Just move between the safe spaces, knowing that any square where the paths intersect will be safe on the next charge. The Hunter of Bardam will also be using Empty Gaze during this, so begin my moving towards it before moving from safe spot to safe spot away from it so you aren't looking at it.
The start of the second trial will see Bardam use Sacrifice, summoning three pillars. At least one player needs to be standing in each circle around the pillars. His next attack, Bardam's Ring, will first target you and then chase you around the arena with Comet, much like Ifrit's Eruptions, so take care to keep moving and not chase your party members. Immediately afterwards the Hunter of Bardam will face a random direction and begin using Heavy Strike, which is a circular AoE except on his rear. It strikes in several bits like Magnetism did, so if you're nowhere near his rear it's possible to stand at the divider and dodge between when it fires, but it's easiest to just be near the Hunter when Bardam's Ring ends. Lastly, he'll use Comet Impact, which is four large AoE circles. There's a safe spot always on top of the Hunter of Bardam, so just run up and give him a hug.
For the third and final trial, pay attention to the Star Shards that fell during Comet Impact. A Looming Shadow will appear and begin casting Meteor Impact and Bardam will use Reconstruct to change the Star Shards on the side of the arena into Warrior of Bardams. Immediately afterwards more Throwing Spears will appear and use Charge again, pay attention to where they hit: Of the two remaining star shards, one will be hit by two spears while the other will be perfectly safe. Take note of the safe one and dodge Charge. Next the Hunter will use Magnetism (without the middle AoE this time, only the outer ring) while the two Warriors will face the middle and ready Heavy Strike. For a brief moment the only safe spot will be in front of the two remaining Star Shards, but you want to be in front of the safe one, the one that was not damaged earlier. Magnetism and both Heavy Strikes will hit both Star Shards, destroying the one that was already damaged. You have only a brief moment to get behind the sole remaining Star Shard to survive Meteor Impact. Once that's done, the fight is over.