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You can catch most of the episodes on Youtube. I put together the following list of all of the episodes with their links from Season 1.
The first season was filmed in 1959.

Mickey Mantle vs. Willie Mays: https://www.youtube.com/watch?v=HaxrzW3aSrc&t=986s

Mickey Mantle vs. Ernie Banks: https://www.youtube.com/watch?v=F44VtFqVnEM

Mickey Mantle vs. Jackie Jensen: https://www.youtube.com/watch?v=vV2Juk2YEHE

Harmon Killebrew vs. Mickey Mantle: https://www.youtube.com/watch?v=2JAMbwIiV80&t=429s

Harmon Killebrew vs. Rocky Colavito: https://www.youtube.com/watch?v=GKq4xdoS4vE&t=458s

Ken Boyer vs. Harmon Killebrew: https://www.youtube.com/watch?v=u0avExaz2Rg

Hank Aaron vs. Ken Boyer: https://www.youtube.com/watch?v=-pZ6Lvddhrw

Hank Aaron vs. Jim Lemon: https://www.youtube.com/watch?v=YBj0isVvfuk

Hank Aaron vs. Eddie Mathews: https://www.youtube.com/watch?v=838ffjJqy2c

Hank Aaron vs. Al Kaline: https://www.youtube.com/watch?v=mhZLtsEPjyo

Hank Aaron vs. Duke Snider: https://www.youtube.com/watch?v=mtkn8oA7QkQ

Hank Aaron vs. Bob Allison: https://www.youtube.com/watch?v=ZqVv1NzMv-Q&t=169s

Wally Post vs. Hank Aaron: https://www.youtube.com/watch?v=0QlJ9EhghFs

Dick Stuart vs. Wally Post: https://www.youtube.com/watch?v=HKLuPCsK83Y

Dick Stuart vs. Gus Triandos: https://www.youtube.com/watch?v=UN9dsm5dhZo

Frank Robinson vs. Dick Stuart: https://www.youtube.com/watch?v=1ZESIXtRz9Y

Bob Cerv vs. Frank Robinson: https://www.youtube.com/watch?v=R7u415RsUjg

Bob Allison vs. Bob Cerv: https://www.youtube.com/watch?v=ziYWmOKlFXc

Willie Mays vs. Bob Allison: https://www.youtube.com/watch?v=zjYdV568NjU

Willie Mays vs. Harmon Killebrew: https://www.youtube.com/watch?v=XBY40L_Rp2U

Willie Mays vs. Jim Lemon: https://www.youtube.com/watch?v=UiHOH8rvjsw

Gil Hodges vs. Willie Mays: https://www.youtube.com/watch?v=ijR6Qt-O0C0&t=3s

Ernie Banks vs. Gil Hodges: https://www.youtube.com/watch?v=xA43r43PZwA

Jackie Jensen vs. Ernie Banks: https://www.youtube.com/watch?v=I1oM-cdFwKU

Jackie Jensen vs. Rocky Colavito: https://www.youtube.com/watch?v=2TPE0RlwYOI

Mickey Mantle vs. Jackie Jensen: https://www.youtube.com/watch?v=OvIOUFov-u8