Wyverns are a Rider-class dragon enemy. The normal wyvern is green.
A Wyvern's regular attack is to swoop in and claw a Servant, while critical hits are distinguished as being a ranged wing buffet. They also have the skill Sharpen Nails (爪とぎ), which buffs itself to increase damage dealt by critical hits. Wyverns use their Noble Phantasm after 5 ticks.
Wyverns are a significant step up from the human/skeleton rabble in terms of health and damage. While there is no specific strategy needed for them, if you know they are coming, take out your Caster Servants and bring your Assassins or Berserkers. Because they tend to have a high critical rate, killing them quickly will minimize the damage your party takes.