Most easily achieved in the main inn Flotsam. Go into the bar and you will find all three activities. This is a very simple achievement.
Arm Wrestling - Move the analog stick slowly in order to keep the reticle within the moving yellow bar. Watch out, it shrinks as it gets nearer to the end.
Dice Poker - Rules are simple for anyone familiar with poker, but a full run down can be found here.
Fist Fight - Simply follow the on-screen button prompts to victory!