There are 2 minecart segments during Chapter 11 that you need to survive without taking any damage. If at any point, you see the cart's health bar in the bottom right corner drop, make sure you reload your last auto-save.
While in the cart, lean left/right into each of the turns to prevent it from tipping over. If there is a wooden barrier in front of you, shoot it with your gun. If you see a track junction, make sure you also shoot it to change tracks. Finally, clear out each of the enemies before they can attack you. Most will drop quickly, but the chainsaw enemy will take many hits. Your goal with him is to make sure he is stun-locked when he is close enough to hit you.
Be mindful of explosive barrels throughout the area which can help clear debris and enemies quickly. Once you complete the 2nd minecart ride successfully without taking damage, the achievement will unlock.