The achievement does not require that all of Blue Team never die; at least one member never dying is enough to grant it. The achievement will not be awarded until the level is fully completed, including the cutscenes, meaning it will be granted at the start of Guardians.
While possible on solo, it is best done on co-op for communication with one's teammates. Should three of the four characters of Blue Team be downed, the surviving character must fall back to a safe place to allow the other players to respawn as quickly as possible. The enemies to watch out for are Soldier Captains with Splinter Turrets, Soldier Snipers with Binary Rifles, and Promethean Knights (especially Knight Commanders) with Incineration Cannons, as the latter two enemies can instantly kill a character and make him/her unrevivable until next respawn, while Soldier Captains cannot instantly kill a character and make him/her unrevivable but are otherwise extremely dangerous with their Splinter Turrets.
Upon reaching the triple Warden Eternal boss fight at the end of the level, it is actually possible to skip it by taking one of the man cannons in the arena, boosting towards the platform that actually leads to Cortana, and then doing a ground pound onto the platform, clambering onto it, and simply running to the room at the end. This still unlocks the achievement, so long as at least one player stays alive during the entire level.
The following criteria will block this achievement from being unlocked: