Overshields are for Sissies
From Halopedia, the Halo wiki
Overshields are for Sissies is an achievement in Halo: Combat Evolved Anniversary and Halo: The Master Chief Collection. It is awarded for completing the campaign level The Pillar of Autumn on Legendary without picking up an overshield. It is worth 10 Gamerscore.
It is possible to complete this achievement along with the "Walk it Off" achievement.
Simply avoid entering the Covenant boarding craft. Due to close quarters of this level, grenades are very useful in both killing and drawing enemies out of cover. Throw grenades while still staying in cover. Burn through the Covenant using plasma rifle on Sangheili and pistol on Unggoy, and one will eventually get to the end of the level. Dying does not invalidate the achievement, so it can be obtained in co-op, using the partner to respawn in the event of death.