Bigfoot is definitely a challenging adversary. Like you say he is superior in most areas and has few weaknesses. The ability to move through opposing fighters and move long distances (both in maneuver and card effects) makes him hard to pin down, and Jackalope is frankly kind of beefy especially with access to a lot of Any cards that keep it from being KO'd quickly or easily. Ranged attackers make his job harder, but they feed his special ability much easier. Extra feint cards also mean your tricky cards are less likely to work.
Other than the fact that good card play in general is necessary to beat him, my advice is to be willing to use your feints on offense. That makes the opponent think twice about when to defend and keeps them from using the cards that let them run away.
Other than the fact that good card play in general is necessary to beat him, my advice is to be willing to use your feints on offense. That makes the opponent think twice about when to defend and keeps them from using the cards that let them run away.