The Bluecoats: North & South

This requires you to win ten total "campaigns" across your time with this game. Note that 2-player campaigns don't count; they must be single player.

Before worrying about this achievement, get Historian (100G) and Great strategist (200G), which will be seven victories, minimum. To get your remaining three, the fastest way is actually the exact same strategy in Great strategist (200G) except playing on Easy difficulty. I have copied the information from Great strategist (200G) here and amended it slightly for Easy difficulty, since you should be winning within three turns, which also unlocks As fast as lightning (100G).
 

• Play as: North (this is the default)
• Difficulty: Easy
• Battles: Inactive
• Attacks: Inactive
• Reinforcements: Active
• Storm: Inactive
• Battle: 1864 (the last one)

The North has a very clear advantage in the battle of 1864, since it starts with three of five forts, and more states controlled. It may sound counterintuitive to turn off Battles, but this eliminates all skill from this achievement. With Battles set to inactive, it becomes a matter of who has more army members to win each fight, and with the steps below, you will always have more than the AI and therefore always win.

Turn 1

• Move your rightmost unit south one state to North Carolina, where the lighthouse is
• Move your second unit from the right down one state
• Press  to open the shop, buy a Job, and place that new unit where the unit above just came from
• Move that new unit one state down to merge it with the existing unit
• Move your northwestern unit (the one on the northwest fort) southeast one state, to the uncolored state
• Move your last unit southwest to merge with the unit you just moved

HERE is a clip of me showing the first turn, so you can replicate it. This is the most important turn since it sets you up for victory pretty easily.

AI Turn 1

• They will always move their southeastern fort unit up to North Carolina and attack you, to try to take this key state. It's a 50/50 chance who wins, since you have equal numbers. On Easy, you will most likely win
• They will attack your merged unit in the center. You have a double unit here so you will always win
• They will move up on the west side. If they attack you, they will lose since you have a double unit. If they don't attack, you will next turn

Turn 2

• Your western unit should attack any remaining enemy unit in range, if any is left. You should be one state away from the southwestern fort
• Your central unit should move south one more state, onto the railroad tracks. If there is still an enemy unit left on one of these southern states, pick the one they're on so you destroy them and also end on a railroad state. If there isn't an enemy unit left, move southeast to the state just west of the southeastern fort. You want to be on the railroad track next to it
• If your eastern unit won at North Carolina, move south and attack the southeastern fort. If you capture it, and no enemy units are left. You'll win. If your unit lost, nothing else to do here

AI Turn 2

• Their train will come. If you are successful in stopping it with your unit on the railroad, they won't get any money and won't be able to deploy any more units. If they succeed, they only get $2, which isn't enough to buy a new unit for them
• Their only remaining unit may by the one on the east coast. It will move up toward the northeastern fort one more state

Turn 3

• By now you should have at least $6 saved up. Buy a unit and place it on the northeastern fort
• Assuming the enemy unit isn't on the state just south of this fort, move this new unit one state south. You should be just north of the enemy unit on the east coast
• Buy a second unit, place it on the same fort, and then move it south to merge with the previous one. You now have a double unit ready to take out the enemy unit on the next turn
• Your western unit should attack the southwestern fort. You have a very high chance to win on Easy
• Your other unit(s) in the south should stay on the railroad but continue attacking the southeastern fort. If you succeed, you'll win next turn. If not, no impact to your unit. It'll return to the railroad state

AI Turn 3

• Their last unit on the east coast will move up and attack you. They'll lose easily. They should have no more units left. They will lose here if you already took one of the southern forts

Turn 4+

• If you still haven't won, spend your money on the Reload item from the shop to increase chances of taking a fort/train, and each unit in the south attacks a fort from a railroad state. Once you take one, you'll win

AI Turn 4+

• They have no units and will just be trying to get money from their train, which assuredly won't be succeeding