What is the ruling on pledging with the words: "May he who betrays the other be punished by his Lord with eternal hellfire, abiding therein forever," and what is required concerning this pledge?

It is impermissible to supplicate for oneself or others to abide eternally in Hellfire, because eternal residence therein is for the disbeliever. This is considered ignorance, injustice, and an transgression in supplication. Such a supplication might coincide with an hour of acceptance, thus becoming a cause for perdition, just as supplicating against oneself, one's children, and one's wealth has been forbidden. This falls under the category of supplicating for forbidden things, which is prohibited. The one who has said this must repent to Allah.