After getting beaten, Heihachi's unconscious form is dropped off a cliff. No sweat. This old man will come rollin' home and kick everyone's ass.
http://www.youtube.com/watch?v=RANLUZYraMo
As I said, Heihachi came back and defeated Kazuya and Devil. We fight Devil and it's never stated anywhere Heihachi ONLy beat Kazuya so...yeah. He then drops his assholey son down a volcano. Definition of PWNED.
http://www.youtube.com/watch?v=9gJhBsa6_rA
And again, Jin's Tekken 3 ending. Heihachi is thrown through a stone wall and dive-bombed. Sits up like nothing happened.
http://www.youtube.com/watch?v=1O-G5rtIGkY
As for Heihachi beating Kazuya, Kazuya agrees Heihachi is more powerful apparently.
“Kazuya believed once he unlocked and controlled the power of the Devil Gene, he would be powerful enough to defeat Heihachi....”
http://www.youtube.com/watch?v=J-AbuvpFFzM
And Heihachi also defeated Kazuya in Tekken 4, before leading him to Hon Maru.
Now Heihachi's most famous feat: after getting blasted across a room by Devil and then beaten by Jin, he gets up and takes out several Jack Units. Kazuya, being the coward he is, leaves Heihachi to get blown to bits. Heihachi however, survives. Notice also how several of the Jacks, each definitely in the multi-ton range, are jumping on Heihachi. Lacking the Devil Gene and he's taking more damage in his lifetime than any of the other Devils in his family.
http://www.youtube.com/watch?v=m_tI_q8qVz4
He was blown "several miles" and on the "verge of death for weeks."
http://www.youtube.com/watch?v=c-wNF5ewguw