There are several was to explain the betrayal of Jesus in biblical context.
One idea is that it was predestined by God. Jesus was sent to die for our sins and so whatever Judas' personal motivation was, he was helping Jesus to fulfill his destiny. He may even have known this, despite his feeling of guilt afterward. This is supported by Jesus' words at the Last Supper:
-[Peter] asked him, “Lord, who is it?” 26 Jesus answered, “It is the one to whom I give this piece of bread when I have dipped it in the dish.”[h] So when he had dipped the piece of bread, he gave it to Judas son of Simon Iscariot.[i] 27 After he received the piece of bread, Satan entered into him. Jesus said to him, “Do quickly what you are going to do.” - John 13
Against this we have the curse of Jesus in Matthew 26:24 "Woe to that one by whom the Son of Man is betrayed! It would have been better for that one not to have been born.” But this is prefaced by "The Son of Man goes as it is written of him." So the idea that it was predestined leaves us with questions about how God would use Judas to fulfill his will, but also condemn for fulfilling his role.
If we want to go beyond the theory that Judas was God's agent to fulfill Jesus' destiny, we have to speculate about Judas' motivation, a motivation strong enough which to use his free will to betray Jesus even though, Judas had witnessed God's power in Jesus so dramatically.
One theory is that Judas was a Zealot who wanted to prod Jesus into action against Rome. For Jews, especially the Zealots, the Messiah did not come to die for our sins but to re-establish the Davidic throne and to do so the Messiah needed to take dramatic political action. Judas' possible identification as a Zealot is indicated by two bits of evidence: his name "Iscariot" may be related to the word for the faction of Zealots know as the 'sicarii,' meaning dagger-men. Also, in the [Epistula Apostolorum[(https://www.earlychristianwritings.com/text/apostolorum.html) vs. 2, [2nd century] Judas is called Judas Zelotes, and appellation usually associated with another apostle, Simon the Zealot. In this view, Judas believed Jesus was indeed the Jewish Messiah who had divine power, and by turning Jesus over to the Romans, he Judas thought he would move Jesus to dramatic action.
The Gospel of John suggests another possible motivation for Judas: financial corruption. John 12 states:
Mary [of Bethany] took a pound of costly perfume made of pure nard, anointed Jesus’s feet, and wiped them with her hair... [But Judas] said, 5 “Why was this perfume not sold for three hundred denarii and the money given to the poor?” 6 (He said this not because he cared about the poor but because he was a thief; he kept the common purse and used to steal what was put into it.)
The narrator makes Judas' motivation clear: he was a thief, and the implication of simple greed may also be attributed to his selling Jesus out for 30 pieces of silver. Conversely, one might speculate that Judas felt Jesus was acting hypocritically. He had taught that to enter eternal life, a rich man had to sell all he had and give it to the poor. [Mark 10:21] But here Judas felt Jesus was squandering a year's wages worth of pure nard on himself. So Judas might have lost faith in Jesus, so much so that he was willing to betray him as a false messiah.
The action of Mary of Bethany in this scene is also suggestive. To care for a man's feet was an extremely intimate gesture, and the use of a woman's hair to do so was scandalous. In addition to possible moral outrage, Judas may even have felt jealousy toward Jesus if he himself had a romantic or sexual interest in Mary.
Finally, we should mention the 2nd century gnostic-christian Gospel of Judas, in which Judas is described as a co-conspirator of Jesus. This work, however is considered heretical Judas, like Jesus himself, is a pre-existent semi-divine being who comes to earth to show humans the Truth, which is that our physical bodies are only illusions from which we need to escape.
-Jesus said to Judas "You'll do more than all of them, because you'll sacrifice the human who bears me. Your horn has already been raised, your anger has been kindled, your star has ascended, and your heart has [strayed]." vs. 56
My answer in summary: there are several ways that Christians might explain why Judas betrayed Jesus despite witnessing God's power in him. They include the he was God's agent in doing so, that he was a Zealot who wanted Jesus to use God's miraculous power against Rome, that he was greedy and wanted money, that he lost faith because he thought Jesus was misusing money, that he was outraged or jealous over Mary of Bethany's intimacy with Jesus, or even that he and Jesus were both divine messengers and not normal human beings.