The First of the Fallen is John Constantine's most dangerous enemy. The First was created by God before the Heavens the Earth and life itself he was intended to be God's confidant and conscience but when The First discovered God's diminishing mental state he was the First banished to Hell. Soon he was followed by The Second and Third of the Fallen. The First of the Fallen assumed that the other two were just as powerful as him and the three became the unholy trinity of Hell but soon were taken out of power by the next banishee, Lucifer the second most powerful being next to God. Lucifer took over Hell for thousands of years before leaving Hell, leaving the unholy trinity in power once again. Although it seems Garth Ennis was trying not to mess with the continuity Neil Gaiman was establishing with The Sandman as The First of the Fallen mentions that The Presence has placed Duma and Remiel in authority over Hell.
The First of the Fallen first came into contact with John Constantine when John was in Ireland looking for a cure to his cancer and discovered that his friend Brenden had sold his soul to The First of the Fallen. John distracted the First when he went to wait and drink in a bar by turning his beer into holy water that caused The First to throw up blood during this time midnight passed and because The First could not collect the soul for Hell it was placed in Heaven. The First decided to get his revenge on John by torturing him in Hell when the cancer took John's life (because John had killed his father, Hell was where he would go after death) claiming John's soul was his "by right of insult" but he was tricked when he discovered John had sold his soul to the Second and Third of the Fallen and slit his wrists, in order to prevent war over over the soul of Constantine the unholy trinity were left with no choice but to bring John back to life with no cancer this became the basis for the feud between The First of the Fallen and John Constantine.
Over the years The First of the Fallen continued to torture John and his friends. The First came to realize that The Second and Third of the Fallen were not as powerful as him and The First killed them both and set to claim John Constantine's soul but this was in fact a long con set up by Constantine and the First was seemingly killed by the succubus Ellie who stabbed The First with a knife made up of the remains of The Second and Third of The Fallen.
The First was in fact reborn as a fisherman retaining memories of his previous life The First and a demon called Buer attempted to con John Constantine, with the demon Buer blackmailing John by threatening his friends and family, John sold his soul to the First of the Fallen and although The First was restored to power he didn't gain all of John's soul but only the bits and pieces he felt best to remove from himself making The First conned again.
The First and John seem to continue to battle but there seems to be no real victor in sight.