Like the title says.... Is it required to have Internet to download Brigmore Witches and the other DLC for the 360 version of the GOTY edition? Or is all DLC available on a 2nd disc and does not need to be downloaded?

With a GOTY, all DLC tends to be on the second disk. Only exceptions are really when DLC is released after the GOTY (Such as Oblviions Fighters Stronghold due to various delays)

It's all on the 2nd disc.

Not always true. The Borderlands 1 goty just gave you the DLC codes to download.
I always ask when I buy gotys now, it's good to know what format they will be in.

Ah, didn't know that one.

Thank you. I wasn't sure since I figured all the DLC wouldn't fit on one disc (even if it was on a separate disc than the main game) but this is good to hear.