I've noticed that quite a few people are having trouble killing wyverns. My advice is avoid using sword and shield as most are pathetically weak. Just wait until the wyvern has charged or shot a fireball, dodge the shot and attack it from the side or behind.

With my Great sword equipped, I advise the draw and slash, running towards the wyvern, then pressing TRIANGLE before quickly rolling the side (with CROSS). I sheathe my weapon to evade, then I repeat the process.