Source: TW
Bhīṣma was literally protected by 8 divine Brāhmaṇas during the battle & they tell him in a dream that night that he is like their own body & they will protect him from Paraśurāma & give him the Prasvapna mantra (which makes the victim sleep).
During the battle next day, Bhīṣma is unable to secure any advantage over Paraśurāma (& vice-versa) & decides to end the stalemate by invoking the Prasvapna mantra. Nārada & other Ṛṣis ask him to not use the mantra as it will amount to humiliation of one’s own Guru.
Paraśurāma is visited by his own ancestors & is told that neither of them will be able to slay each other (in Bhīsma’s case, because of the boon given to him by his father). After some high-level negotiations by the sages, the story ends with Bhīṣma offering pūjana to Paraśurāma.