Beowulf is encountered as the level boss of Mission 11. The goal of this fight is to kill the boss during the light explosion sound. Most of the time, this fight depends on good JC's and the strategy is strict. Beowulf is also part of the boss rush in Mission 18 and the strategy still remains the same.
If Vergil doesn't get enough JC's from Aerial Rave then either he will have to JC's with Beo more or chase him with more Aerial Rave.
If Dante doesn't get Release-Kill or JC's from A&R then he will have to chase him for more Aerial Cross
Dante should enter this fight with 1.5 Rage-meter to speed up the process. He can still Guard his attacks for the Release-Kill build up.
Aside from RG, Vergil can follow the same steps. His Yam Aerial Rave with PS can kill him in one cycle. Because Beo is weak to Yam.
This is ideal fight with Dante.
Ideal fight with Vergil