Piece of advice, people: Despite what the lower ranks may teach you, Burst Attacks are rather easy to mitigate. Sure, they do significant amounts of damage, but that's only on the second stage, and the second stage only happens if the first stage lands a solid hit.
So, what are your options? Either shield once the cutscene starts, get in a attack to stagger them first, or just plain dodge that initial hit. Incidently, the second stage doesn't occur if you manage to KO your opponent with the first stage.
And on the topic of Burst Attacks, the award for "Most Excessive Hit Count" is... Shadow Mewtwo! I may not have an exact count, but it was 4 digits and started with a 9. It also wouldn't surprise me if the actual total was 9999...