Does Biggs's ability to shift one point of damage work against Fett's ability to cause one point of damage every time it activated against one engaged squadron? Aka can Biggs shift that point of damage to another squadron within range one?

No because Boba's damage isn't an "attack."

As CaribbeanNinja stated, the short answer is no as Biggs ability is "during an attack" and Boba's ability isn't during the attack, is just when he activates.

Also just to clear things up, Boba's ability doesn't work only for engaged squadrons, they just need to be at distance 1 (this means that you can damage also a squadron for which your LoS is obstructed and therefore are not engaged), and also can work with a ship at distance 1.

Thanks again!

Ace, this answers a similar question I had on thursday re mithrals movement damage and biggs.

Luckily we came to the correct conclusion in the game, but nice to have it confirmed.