Hullo Mr. Gatling: Full Sync Blitz
This project started out as a full sync guide and evolved into a speedrun. I demonstrate how to mow down Blighters, not how to pop in and out of cover. The result is the same: 100% synchronization.
Don't take any damage
The first thing you should know about getting full sync is that "Don't take any damage" only applies until the train pulls away from the station. Don't get discouraged. That's less than 2 minutes (in this video it's only 1:25).
The second thing is you should take advantage of "Reload last checkpoint". Doing so will give you more time to unjam the gun and take aim. The first wave of blighters will run down the hill across the tracks where they can be picked off before they get into position.
Memorize the order in which the Blighters arrive. They don't shoot until they reach their position and have time to take aim. If you can kill them in order it isn't hard to stay ahead of them and not let any get off a shot. Also, try to save explosive crates for later.
Snipers
When Nigel says, "They're on top of us." a series of three snipers arrive. The first is on the roof to your right, the second on the train station roof to your left, and the third back on the same roof as the first. This is a good time to use explosive crates for the Blighters on the ground. It gives you more time to aim at the snipers.
Taking Cover
If you're in a tight spot you can hold 
to take cover. While in cover, use the right thumbstick to rotate your view toward your next target (NB: This memory uses all right hand controls. Reach over with your left thumb while in cover.) You can't get a precise aim this way but it will help you aim more quickly when coming out of cover. Wait until you hear a shot and then release , aim, and fire.
This works best when there's only one Blighter remaining in the wave. When there are more than one, they often fire simultaneously so you can exit cover, shoot, enter cover, repeat. I don't have much experience with this. Your mileage may vary.
When he says, "Driver! I believe it's time to go!" take cover and hold it. This is when your train pulls away from the station and a huge wave of Blighters appear. You don't have to shoot any of them. "Don't take any damage" is replaced with "Detach 5 wagons".
Detach 5 wagons
Most people don't have any problem with this objective, although it can be difficult to aim because both trains are moving. Be sure to aim to the right at the next coupling before you come even with it. It isn't necessary to kill the Blighters on the train (no penalty for taking damage at this point). On the fourth and sixth wagons, you can detach them by shooting the adjacent explosive crate.
Unjam the gun
If you lean on the trigger too much the Gatling gun overheats and you have to unjam it again. I'm not sure what the exact formula for overheating is but it's based on rounds recently fired (e.g. 4 seconds of continuous fire), not total number of rounds since the beginning of the mission. If you fire in short bursts it's possible to complete the whole mission without ever unjamming again.
Destroy the dynamite crate
The first carriage is full of dynamite and the second carriage is full of Blighters. Well, three of them anyway. These Blighters have never shot me while I took aim at the dynamite. However, they always shoot after the Gatling gun catches fire. That's why I killed two of them earlier. The remaining one took a shot at me which I dodged.
It wasn't until after this video was edited that I realized I didn't take any damage throughout the whole memory. Maybe it's not impossible after all...