Beowulf emerged victorious by killing the monster.

Beowulf ascended the throne after the demise of Hygelac, former king of the Geats. He ruled for fifty years until he was forced to face a dragon. The dragon was agitated and wrecked havoc on everyone because a golden goblet was stolen from its den.

I would carry neither weapon, nor sword against the serpent, if I knew how I could make good my boast with such an enemy, as I did in the day of Grendel.

Beowulf killed the dragon, however, he also succumbed to wounds caused by the battle.

He struck the loathsome monster a little lower; his bright and burnished sword penetrated; the beast's blaze began to dwindle.

Beowulf spoke; he knew full well that his portion of earthly bliss was done and gone, that the tale of his days had fled, and that death was near.

While the Danes are celebrating the death of Grendel, there is a tension that informs the reader that all is not well. There is a foreboding danger. Although Beowulf has defeated Grendel in a very important battle, there is a sense in the celebration feast that something more dangerous is about to happen:

At the feast, poetry is sung not only of Siegmund, a positive example, but also of Finn, who was supposed to be quite the opposite. Could this be foreshadowing that all is not well in Denmark?

Clearly, the most important battle is yet to happen. Grendel's mother comes to avenge her son's death. Grendel's mother carries off Hrothgar's friend and counselor. For this reason, Hrothgar is broken hearted. To kill Grendel's mother would be a most important battle because Hrothgar would be avenged of his close friend's death:

While the Danes are sleeping, Grendel's mother comes to avenge her son. She carries off Aeschere, Hrothgar's friend and counsellor, a man who had always stood at his side in battle. Beowulf finds Hrothgar broken with grief over the loss of his friend.

In a most important battle, Beowulf kills Grendel's mother. Now, Herot would is safe from all harm of monsters. No doubt, this is a most important battle for now the Danes can live in peace. 

After Beowulf kills Grendel's mother, the Danes are rid of the horror associated with Grendel and his mother. When Beowulf kills Grendel, it is a major victory. Because Grendel's death brings about the presence of his mother, it is very important to kill Grendel's mother. With Grendel dead, his mother was still a threat to the Danes. No doubt, killing Grendel's mother was a major battle. Now the Danes are free from all harm.

The Danes can live in peace because Grendel and his mother are dead. When Beowulf killed Grendel, it made his mother angry. Grendels' mother was more of a threat than Grendel. Beowulf had a difficult task in killing Grendel's mother. Therefore, this battle was a most important one. 

Beowulf, in the tradition of much heroic poetry, consists of a "main" narrative and a number of short digressions, included to keep the audience's interest. The main narrative—that is, the story of Beowulf himself—can be divided, however, into three key sections or, as you say in your question, plots.

Each of these plots requires Beowulf to slay an enemy. First of all, he comes to the aid of Hrothgar and swears that he will put an end to the killings being wrought by Grendel, the monster. Beowulf is true to his word, and Grendel is slain. However, in killing Grendel, Beowulf has aroused the ire of Grendel's mother, arguably even more terrible than her son. The second "plot," then, culminates in Beowulf killing Grendel's mother and leaving, victorious, for his home land.

The third section of the story does not end so well for Beowulf. Partly in a bid to ensure his exploits will live on after he dies, the now-old Beowulf, who has become king, must slay a dragon that is terrorizing his people. However, he dies in the process, and the poem ends with Beowulf's people cremating his body.