Bring lots of stimpacks.
Get the Cowboy Perk to deal additional damage with Dynamites and the Cowboy repeater.
Get the Fast Reload Perk to shoot faster with the Cowboy Repeater.
Get the mods for the Cowboy Repeater, notably the one that makes shooting faster and the one to get the gun to hold more bullets.
The result is that with the Fast Reload Perk and the mods, the cowboy repeater becomes a semi-automatic weapon that destroys anything in its sight.
With a high explosives skill and the Cowboy perk, Dynamites deal a lot more damage than grenades.
...And aim for the head!
I did the whole game with only cowboy-related equipment and the sheriff duster. Some parts were difficult, notably the BOS bunker, but lots of stimpacks helped there.
http://i72.photobucket.com/albums/i185/DarkBrotherhoodmod/Sheriff.jpg