Are you sure you want us to spoil the story? Well DMC2 has not the best story but it would be better to see it for yourself. Anyway here's the story...read only if you really want
Dante meets Lucia...another Devil Hunter like him who wants him to visit Vie de Marli in order to be hired from an enigmatic old woman named Matier. Matier almost died from a sudden explosion probably caused from some servant of the bad game's vilain. Anyway Matier survived and offered Dante a deal; he stops Arius(a president of a company that uses the demon power)and she tells him the true story of Sparda, since she purposedly met him in her younger days. Dante flips a coin with Trish in order to decide and says ok to the offer. He and Lucia are to gather some mysterious artifacts called the Arcana which are necessary for Arius' goal to contanct the former demon king Argosax and receive his power. They find the artifacts after some missions but Lucia decides that killing Arius is the best she could do so she tries to do that and fails. Arius who had seen Dante throughout the game tells him to trade every Arcana for Lucia. Dante obeys and gives him the 4 Arcana, a Dagger, A coin, A glass and sth like an Artifact. But the Argosax isn't summoned since Dante switched the coin with Trish' coin. Dante defeats Arius but he's forced to escape in order to save Lucia. Arius manages to get the Arcana and little by little he turns everything into demonville

Dante decides to fight him for the last time and goes to his company killing him and taking the Arcana. But the ritual to open the gate to the demon world is opened and Dante who actually knows what Sparda did, and just helped Matier for duty, decides to enter. Lucia admits that she was made by Arius and that she is better off throwing her life in the demon world crying. Dante tells her that Devils Never Cry (how unlike him:lol: :lol: )and enters the demon world to duel Argosax. Argosax is a fusion of various other bosses but is defeated easily by Dante. Then Despair Embodied emerges from Argosax's core but Dante defeats him too(in a stylish way)then he uses a motorcycle that he frequently has throughout the game to continue further to the demon wotld where he defeats Possessed Arius and the true Argosax. Slightly before he beat them the door to the demon world was supposedly closed and Lucia thought that Dante was lost. However we hear a motorcycle parking near the place in which Lucia was waiting...meaning that probably Dante escaped somehow.
That's it, hope u like it(there are various sub plots like a boss that had fought Sparda in the past that I left them since they aren't that importand to the story )