In 2367, Amasov commanded the Endeavour in the Battle of Wolf 359. In what he perceived to be his final moments, Amasov transmitted his analysis of the Borg: "In all my years I could never imagine terror such as this. Cold. Calculating... Murderous. It is just a matter of pure luck that any of us are alive right now. The Borg are as close to pure evil as any race we've ever encountered."
Miraculously the Endeavour survived the battle, the only ship to do so, and at the cost of half her crew. Amasov stayed in a hospital on Earth for some time following the battle. While still hospitalised, Starfleet held a hearing to discuss whether or not Jean-Luc Picard should be allowed to return to command following his role in the Borg attack. Amasov's log was played in the hearing as evidence against the Borg and, by extension, Picard. (TNG comic: "Loyalty")
In the same year, while studying information about the Borg in preparation for an anticipated encounter with them in the Delta Quadrant, Kathryn Janeway reviewed Amasov's and Picard's logs of their encounters with them and quoted Amasov's appraisal of the Borg to Chakotay. (VOY episode: "Scorpion")
In 2379, Amasov attended a briefing on a new Borg attack, in which they used a time wave to assimilate all races throughout time. The group of Starfleet officers, including Janeway and Picard, discussed the Borg's objectives and formulated a plan to stop them. (TNG comic: "Alien Spotlight: Borg")