ANSWER: Before we delve into if Judas did repent of betraying the Son of God let us take a look at the man himself. He certainly is one of history's most unfortunate figures. He became a pawn in Satan's evil game to totally destroy the Son of God. Satan's plans, however, to kill Jesus FOREVER totally failed as was predicted in the very FIRST prophecy of the Bible (Genesis 3:14 - 15).
What kind of man was Judas Iscariot? There is an old tradition that says from childhood he and Jesus had been friends and that Christ continually had to pull him out of trouble. Although this tradition may not be quite true, it is logical to conclude that the two were more than mere acquaintances.
Let us take a brief look at Judas' life and personality during the ministry of Jesus. He was, of course, one of the twelve apostles (Mark 3:14, 19; Matthew 10:4) whose surname Iscariot is believed by some to mean 'man of Kerioth.' He was in charge of the group's money (John 13:29) and was a thief who regularly stole from it (John 12:6). Judas was known to be a liar (John 12:3 - 6) who was also deceitful and greedy (Matthew 26:14 - 15).
He was called a traitor (Luke 6:16) and was identified as a betrayer during the last Passover (John 13:21 - 26). He was willing to pretend to honor someone for his own selfish purposes (Mark 14:44 - 45, Matthew 26:49).
Jesus referred to Judas as a devil (John 6:70) and a son of perdition (John 17:12) who it would have been better if he were never born (Matthew 26:24). It is interesting to note that Jesus not only knew he would be betrayed, he hand-picked the betrayer!
70. Jesus answered them (the twelve disciples), "Did I not choose you twelve, and one of you is a devil?" (John 6:70 - 71)
Iscariot was possessed personally by Satan the devil during the last Passover (John 13:27). He betrayed the Lord for money (Matthew 26:15) to those who HATED him and want him dead (Matthew 26:3 - 4). He felt so bad after betraying someone who was innocent that he tried to return the bribe money paid him (Matthew 27:3). His self-hate grew to a point where, even after trying to return the bribe, it led him to commit suicide (Matthew 27:5).
Did Judas repent just like Peter? This act, in the Greek, means "to think differently." If one thinks differently, one acts differently. Godly sorrow leads to changing one's ways but the sorrow of the world (i.e. of human nature apart from God) leads to death as way stated by the Apostle Paul (2Corinthians 7:10).
We know that he felt remorse for his actions (Matthew 27:3) and knew he sinned. His sorrow, however, did not lead to true repentance and a change of heart and behavior. Like him, Peter was also very sorrowful for what he did, which was to deny he even knew Jesus three times (Luke 22:55 - 62, see also Matthew 26:69 - 75; Mark 14:66 - 72; John 18:17, 25 - 27).
Note that although Peter wept bitterly over what he did (especially since Jesus looked directly at him after the third denial!) he did not take his own life. His godly sorrow lead him to deep introspection which then lead to a complete change of heart (see Acts 2). Peter had the kind of sorrow we all must ultimately have if we are to live forever. Judas did not repent like Peter because they did not have the same kind of sorrow and therefore did not produce the same outcome after they confronted their sin.