Wolverine VS Big Barda

Can the "best at what he does" beat down this titan of a woman with her Megarod(no beams though)?

Nope. Barda will mess him up.

Big Barda, no contest

" Can the "best at what he does" beat down this titan of a woman with her Megarod(no beams though)? "

Barda will spend more time wiping the blood off her armor than the actual fight

Barda Stomps

Barda would beat him to a total pulp then take him back to New Genesis to confirm if Logan was related to Oberon.

Hell no.