Bigfoots are tough creatures. They have a rock attack that will demolish most tanks in seconds, while having a claw attack for those high-dodge units. One may choose to have a high-ranked Puma or a Heavier Tank. Either way, the bigfoots will destroy them without much difficulty. The recent update has tweaked the bigfoots, making them far easier to defeat.
An effective way to kill bigfoots is to use splash damage or flame damage or both, such as a Heavy Chemical Tank. It's also good to have units that have crit against critters, such as the Big Game Hunter. They have high dodge and defense, so the tanks would mainly be for defense purposes.
Another great way of killing bigfoots is with aircraft. Bigfoots can't hit aircraft with their rocks, so if you use aircraft with air-to-ground attacks you are guaranteed to win.