Beowulf and Achilles are both powerful royal males who are the subjects of important epic poems. Beowulf is the focal point of the Anglo-Saxon epic poem that bears his name, whereas Achilles is the focal point of Homer's Iliad. Unlike Beowulf, whose parents appear to be mortal, Achilles has one mortal parent (his father) and an immortal parent (his mother Thetis).
Both heroes have significant physical challenges that they must overcome. Beowulf battles a gruesome marsh-dwelling creature named Grendel, while Achilles has to defeat a number of dangerous warriors who are either Trojans or are allies of the Trojans.
After Beowulf defeats Grendel, he must battle Grendel's mother, also a monstrous creature, and then finally he defeats a dragon. Although Achilles never battles a dragon, he, like Beowulf, does fight against and defeat a dangerous female, the Amazon woman Penthesileia.
Beowulf defeats the dragon, but in the battle suffers a wound that ends his life. Achilles dies before the Trojan War is completed, but not from a wound from a dangerous monster, but struck in the foot by an arrow from the most effeminate of the Trojan warriors, Alexander/Paris.
We might also keep in mind that Beowulf's three major battles come over a span of his lifetime, whereas Achilles' most famous victories--his defeat of Hector, Penthesileia, and Memnon--and his death at the hands of Alexander/Paris all come in the tenth year of the Trojan War.