What fighter who won 3 or more titles beat the best competition to get those belts

Intriguing question. Armstrong beat Barney Ross and Lou Ambers, both in the IBHOF. Petey Sarron may well be a future inductee there. Of course these were all for undisputed championships.

Ross won two titles at once by decisioning Canzoneri, then a third over McLarnin.

Duran beat Buchanan, SRL and Barkley. The first two are in the IBHOF, and I'd expect the Blade to eventually gain induction by virtue of his own triple crown status.

My inclination would be to favor Armstrong, after looking up all the triple crown champions to this point in time. I think Sarron was clearly superior to Barkley, having ultimately prevailed in his classic rivalry with ATG FW Freddie Miller, and unlike Ross, Hank did it in three separate bouts, none of them for "*******" division championships.