Minimizing the pain in Biceps and Shoulders due to Mountain Cycling or Offroad cycling
Four factors I can think of


bike
tires
riding style 
conditioning


If the bicycle has full suspension then less vibration.  Carbon frame will absorb vibration.    The fit of the bike is a huge factor.

Larger tires at lower pressure will absorb vibration.  Can run tubeless tires at lower pressure.   If you are running smaller tires then go to a bigger tire like 2.2 - 2.4 if your frame will allow.

Riding style has a lot to do with arm and shoulder fatigue. Try and relax. Move your body forward and back. Don't muscle the bars. Get in the middle and let the bike rock under you. Even if you can just learn to relax between the ruff sections you will gain a lot as the muscles get a chance to recover and get more blood flow.  Watch a good rider on ruff downhill - they are relaxed and a beginner will be tensed up fighting it the whole way.

The more you ride trails the more you will condition those muscles.  In the gym push up, pull up, fly, ...  Whatever is sore find the exercise that engages that muscle.