Engage the rebels in the bridge and take them out one at a time using your arcgun. Avoid staying behind the wooden covers since they can't protect you for long. Keep killing the rebels until you reach Hasting's carriage. After clearing this part of the bridge, interact with the carriage and keep smashing the X button so your allies can pull Hastings out. After this brief scene, Galahad will stay behind and engage the rebels.
Quickly find cover and kill the rebels. You have to move from spot to spot to "spawn" the rebels. Keep doing this until you cleared them out. Next, find a cart that you can use as a ramp and jump over the fence to the next rebel-infested area. Move to the next entrance where a rebel with a hand cannon will appear on top of a rail car. Fall back and hide behind solid cover to avoid getting splash-damaged. Kill the rebel to proceed with the story.
Galahad will then proceed and pick up the hand cannon from the killed and he'll be able to use it in clearing the next rebel-infested portion of the bridge. You can't crouch behind cover so remember to get behind the metal plate on the side of the rail car for cover. When using the hand cannon, do not aim for the rebels but aim for anything solid near them like the ground or walls. This weapon can take out multiple enemies in well-placed shots. After clearing all enemies, a scene will take place.