From Halopedia, the Halo wiki
Marine squad Hacksaw request immediate Spartan assistance after coming under heavy fire from Covenant forces. Commander Sarah Palmer acknowledges and sends in Fireteam Crimson to reinforce the embattled marines. Shortly after arriving, Spartan Jared Miller points to three different locations Hacksaw units are holding up. After Crimson rescues the first group of marines, the bulk of Hacksaw is temporarily re-assigned under Spartan command to support Crimson in their rescue operation. After rescuing the other groups of Hacksaw, Spartan Robert Dalton request the area to be cleared of Covenant reinforcements in order to send a Pelican dropship for extraction. After clearing the area, Crimson and the rest of the surviving marines are directed to the top of a Forerunner structure for retrieval. Before the Pelican arrives however, a pair of Phantom gunships arrive, one of which is carrying a small contingent of Sangheili warriors. Crimson eliminates the group of Elites as well as the Phantoms before Dalton's Pelican arrives for extraction.
When the player approaches the near-left squad.
When the player approaches the near-right squad.
When the player approaches the far squad.
After the player dispatches the Covenant attacking the first squad:
After the player kills the reinforcements.
After the player kills the second group of attackers.
After the player kills those reinforcements.
After the player kills the Covenant attacking the third squad.
After the player rescues the third squad.
After the player eliminates the last reinforcements.
Phantom deploys the Wraith.
After the Wraith is destroyed:
Enemy Phantom unloads more troops. Crimson kills most of them.
After the player nearly clears the area.
After the player kills them all.
When the player reaches the top of the tower.
After the player destroys the last Phantom.
Or, if there are any enemy troops remaining:
If the player saves two or more marines:
Or, if the player saves only one marine:
Or, if the player fails to save any marines:
A Pelican lands atop the tower.
Completing the level with at least one surviving Marine on Heroic or harder will unlock the No One Left Behind achievement.