Bearhugs

Core is most important. Even as a thick guy, my core is tight as hell, helping my muscles communicate and work in tandem. Without that, it's all isolated and regardless of my opponent's size, I won't outlast him.

Arms, chest, legs if you wish to keep them suspended

Hi Mr.Squeeze,
Arms, I guess. They can never be too big......lol

I was wondering what muscles are used during a bearhug, and which ones i should workout the most in order to give the best squeeze

Without a doubt, arms, back, abdomen hard and strong. And, of course, big, strong and resilient chests.