How do I train for a race like “Tough Mudder”?

As for any competition, training needs to include the use of similar movements and muscle groups. Some trainng can be movement specific and some muscle specific. For an event like a “mudder”, it would really be helpful to find a way to duplicate conditions and challenges. You can look to see if there are outdoor facilities in your area that specialize in this type of training or find places that recreate the conditions yourself. But be very careful in seeking out outdoor sites. Unsupervised outdoor activity is oftne dangerous. Never do such training without a partner or group. Always be sure that you can contact emergancy assistance should it be necessary. Safety first.