Warp back to Chuparosa and visit Landon in his favourite cafe for a few games of poker. Keep an eye on the screen for the controls if you've never played poker before; otherwise remember than LT/L2 and RT/R2 allow you to view your cards and 'the flop' respectively.
Whilst betting small seems a cautious way to go, betting with larger amounts can force the AI to 'fold' their hands early on, giving you the two required wins much more easily.
Winning will cause your opponents to call you out for a duel! Duelling isn't too difficult (especially if you've already tried this anytime before now in towns such as Armadillo). The main things to remember is to use the right stick to get your hand closer to your gun and then wait for a second or two before drawing your pistol.
You'll automatically enter Dead Eye mode, so use the time to line up a couple of chest shots and - ideally - a headshot as well. Press fire and watch your opponent drop to the ground. Another opponent steps up to the plate, but this time he's holding a hostage close.
Switch to your Dead Eye again and get a single pistol shot lined up with his head and fire a single bullet into his face. He'll crumple to the ground and the hostage will remain unhurt. Now a bunch of Muller's men will come after you, so take some cover behind any nearby walls.
Use your rifles and/or pistols to dispatch them as quickly and as safely as you can. Don't be afraid to keep your head low if you need to recharge your health!