Barras opens with a BP-expending Invigorate and attack combo, causing his attack to deal massive damage, but leaving him open on the next turn. If he uses Invigorate until his physical attack power can no longer increase, he will explode and deal heavy damage to everyone until it KOs himself first.
In the subsequent fights later on, Barras will repeatedly explode with Invigorate when he is at low health, damaging both parties. This can quickly KO the party, and is quite difficult to out-heal.
Defaulting on the first turn can help protect Tiz and Agnès from Barras's initial attack, and allow them to use Brave freely on the next turn to take advantage of his inability to attack.
The party should use Default as necessary to lighten the damage of his attacks, healing with Treat or Potions as necessary, and when Tiz and Agnès have full Brave, unleash a full attack on Barras. If he still survives, the party should press the offensive to keep Holly from healing the damage he's taken. Once Barras falls, Holly should not be much of a threat.
In later fights, one strategy to mitigate the damage is to have at least one member use Utsusemi several times during the phase where Barras repeatedly explodes with Invigorate, as this will allow the player to evade the blast, while Barras continues to hurt himself until he is defeated.