Defense[]
Beowulf's aggressive style requires a considerable early defense. Not only are the evil troops fast to arrive, but they can also cause serious damage by circumventing groups of defenders and start working on vulnerable buildings.
Sealing off the keep and as much land as possible is a priority against harassments, so get walls up quickly. Walls in particular can stop most of the raiders Beowulf sends against you and keep guards at outlying buildings, preferably quarries and mines. Beware of the demon's wall-jumping ability and the Saxon warrior's brute strength, so have at least crossbowmen and some hefty troops of your own ready. With a stable defense of this combination, Beowulf's raiders are reduced to "walking glory points".
Use the same principle against the siege forces of Beowulf. Due to the sheer amount of light troops, he falls easy prey to crossbowmen and other durable units. Try focusing his siege camp in order to prevent annoying siege engines from coming out.
Finally, the black dragon Beowulf loves requires a precaution of its own. Since it is usually sent directly at an economic quarter, it's best to prepare a few engine towers with dragon harpoons and missile defenders. If playing Ice, the Ice Queen can work wonders, as her ice ray can freeze the dragon, providing ample time for your ranged units to bring it down.
Offense[]
Beowulf's castle can crack pretty quickly before an organized attack. Even though he has lots of units swarming around, they are usually not a threat due to their frailty. Saxon warriors are however just as numerous, and Beowulf can churn them out easily with his economy standing.
Amass an army of sturdy units, most notably crossbowmen and armor just outside of Beowulf's castle, then start pushing slowly. With such a defensive formation, crossbowmen can eliminate nearly every unit Beowulf throws at you. If the black dragon is hatched in the meantime, try focusing it while moving out of burning ground. Also prepare a siege tower and roll it forward, which will be used later to dock at the walls.
When arriving under the walls, watch the fire drakes, as they can still burn through your troops. Dock the tower and scale the walls with your army, eliminating any resisting unit in the way. The layout of the castle should allow you to move freely around, bringing the towers and the gates under your control. When the interior is contained, move in with a few melee units to kill Beowulf, mopping up his guardian werewolves he might spawn.