Instructions
Complete the 72 hour mode without being knocked out by the cultists. Cultists wear yellow rain jackets and green face masks and tend to stick together in large groups. They have a gas attack that can knock you out, which makes getting the Unbreakable achievement impossible. Avoid the cultists or shoot them from a distance while you're completing the 72 hour mode. If they do knock you out, restart from a previously saved game to keep it possible to get the achievement.
Begin overtime mode immediately after you complete the 72 hour mode. The game will automatically shift into this mode and the cultists will disappear. In their place will be special forces troopers. If they damage you enough so that your health bar empties completely, you will be knocked unconscious and wake up a hostage, which would also negate the Unbreakable achievement. Save your game frequently during this mode, as that will allow you to reload a game to a time before you were knocked out.
Complete overtime mode without being knocked out to earn the Unbreakable achievement. Go to your hideout and look around the area near the air duct. You'll see brown paper bags for previously unlocked clothing. The Mega Man Boots are in a paper bag right next to the air duct, so click on the bag to wear them.