I put together a rather lengthy "lessons learned" for playing the Union on Legendary:
Know the time limits of your battle. You can find these either by playing custom or historical battles or watching a youtube video.
Maintain battle lines and protect your flanks with skirmishers
Use roads for rapid movement
Keep your general close to your forces
Build up a reserve of high ranking officers (Colonel or above). This should happen naturally as wounded officers return to the officer pool.
Have spare commanders who you can use to replaced wounded or dead officers when you have the chance to return to camp.
Have spare money or supplies you can transfer to another Corps if necessary. Build up 3 Corps with a minimum of 35,000 in supply. Then boost 2nd Corps to somewhere around 45,000.
Commanders can be replaced (if they are in Reserve) when you return to Camp in a multi-day battle, just as supplies can be shifted from one Corps to another.
Support your infantry with artillery. Do not leave them behind when advancing. In fact, the opposite holds true, move them up first before advancing your infantry.
When charged, if you have a nice battle line, have the brigade that is charged fall back so that multiple units will fire on the charging unit. This is a critical skill to learn.
When “flanked” do not move the unit... have it fall back until they are no longer flanked. A flanked unit that turns it's back on the enemy due to a movement order will break almost immediately if it is also under fire from the front.
Have reserve units which you can swap with heavily engaged brigades during the battle so that reinforcement in the Camp will not require a huge investment of money.
When swapping out brigades on the battle line, do not wait for the new brigade to take its place on the battle line before ordering the other to fall back. As the new brigade gets close to the line order the brigade in the battle line to fall back, thus avoiding a merging of the two brigades (which makes it difficult to figure out who is who) and causing adjacent brigades to start shifting about and throwing your battle line into chaos.
Use the “run” order sparingly and over short distances. If they have to run long distances to get to a critical area of the battle, they will arrive exhausted and be of little use.
When you have the enemy on the run, press them hard so they cannot recover their morale even if they become exhausted.
When flanking an enemy do not order brigades to go all around the battle line to take a position at the end. Shift your brigades sideways and open up a slot for the new brigade to fill to maintain the battle line.
When charging a fortification, use at least 2 brigades to assault each specific location. A third unit should be placed directly behind them so as to be able to fire into the melee in support.
Using 2nd Corps as your primary fighting Corps is a good idea because if you have more than 35,000 in supply, you will have 2 ammo wagons on the field of battle.
Do not give untried recruits good weapons. Set parameters for who gets what. My parameters were 25-30 efficiency before they got a better weapon than the stock Springfield. I also set 40 as the minimum efficiency level to give very good weapons to my brigades.
Don't go crazy trying to build super elite infantry as the Union. A 2 star brigade with 50 efficiency is good enough. Don't waste money on veterans to keep them higher.
Re-enforce your okay brigades with veterans first. You want to build an army that is good overall so when you have the chance with say a brigade with 28 efficiency, give them veterans so they can maintain that level.
When re-enforcing more veteran brigades, re-enforce the brigades which require the least amount of investment first. Set your parameters and then see if you can do so with just recruits. If not add a few veterans and then pump them with recruits.
Remember that in most battles the 1st and 2nd Divisions will bear the brunt of the fighting.
Build up 2 strong Corps with good veterans in the 1st, 2nd and 3rd divisions. The fourth division should be okay troops and many times they don't even make it into the battle.
You want 2 types of artillery: close and long range support. In the beginning use 10 pdr Ordnance for long range support, they are plentiful and cheap. The 6 pdr Field gun is fine to start with as a close support weapon. Watch your reputation for 24 pdr Howitzers and buy them at every opportunity at the beginning of your campaign. They are the gold standard for close support artillery. Later in the campaign you will have the opportunity to buy 20 pdr Parrots with your reputation... buy every gun you can get your hands on. Towards the end of my campaign, my artillery was mainly 20 pdr Parrots, 24 pdr Howitzers and 10 pdr Ordnance, in that order.
When you get good guns, give them to experienced artillery brigades and start new brigades with the other weapons.
Always remember when re-enforcing your army after a battle to check to see if any artillery brigades took casualties. In the Camp phase, when I began re-enforcing my army, I always started with the artillery and they almost always were given veterans.
Use good officers right from the beginning when you start a new artillery brigade. Good artillery brigades will increase efficiency faster than the officer who commands them. So, you should put at least a good Colonel, if not a low grade Brigadier to command new batteries.
In battle, keep your close support artillery right behind your infantry so that they can fire canister at any charging Confederates. They need to be close enough to support but far enough away to let your infantry brigade fall back a bit, if necessary, so as to get multiple units firing on the charging brigade.
Long range artillery needs to be placed on the “hinges” of the battle. To be truly effective they should be firing into the flanks of the enemy. So if you are attacking their flank, first have them in a position where they can fire into the flank of the enemy opposing your infantry's flanking attack. Once you have turned the flank, place them so they can fire into the flanks of the enemy's main battle line. The correct use of Long Range Support artillery needs practice and experience but if they are just firing at units at your front, you are using them incorrectly.
Very experienced Long Range artillery is quite good at counter-battery, nevertheless, it takes time to destroy an enemy artillery battery with counter-battery. Engage in counter-battery only if you have no other unit which is presenting its flank.
When you run into or are attacked directly by enemy artillery, always send out skirmishers in defense. Skirmishers are the number one way of killing artillery.
If your battle line does not provide adequate coverage of the map, place skirmishers on your flanks. Two units is a minimum, I prefer 3. By putting skirmishers on your flanks you avoid nasty surprising attacks on your flanks.
When entering a forested area with your main army, send a line of skirmishers ahead to scout for you.
Once you have the battle “controlled” use skirmishers to clear areas of the map that you have not seen that could possibly be occupied by enemy forces.
When flanking an enemy, use skirmishers to get into the rear of the enemy. They move fast and are capable of routing enemy artillery batteries and capturing supplies.
Do not expect a skirmisher unit to do a lot of thinking. Spread them out in lines and when a target presents itself, “rope them” and order them to attack. Expect that they will attack one time and then fall back. If the skirmishers are in the enemy rear or flank, it is worth micro-managing these troops. So expect to be constantly placing them in a line position and then ordering them to attack. You want to first put them into a line position (or close to it) because when you order them to attack you do not want one unit to block another from firing.
If you are outflanked, the fastest way to stabilize the situation is to send skirmishers because of the speed of their movement.
When an enemy brigade routs, if the area is clear, send out a skirmisher unit or two to keep firing on the routed brigade. I have totally eliminated enemy brigades who routed with 3 skirmisher units.
Use skirmisher units to “push” routed brigades in a direction which is advantageous to you.
When surrounding the enemy, many times the fastest way to close the trap is by using skirmisher units due to their speed.
When you order a brigade to send out skirmishers and they are in the battle line, order the skirmishers to fall back first, or they will be shot in the back and rout.
Cavalry and specialized skirmisher units
While these units have utility on the battlefield, remember they have their own way of maneuvering and singly you must control them continuously. Do not expect these troops to work miracles.
The best way I found to control Cavalry and specialized skirmisher units is by creating a dedicated division for them and use their division tab to select them all and move them as a group.
Expect them to fight just like regular skirmishers, therefore, expect that you must be constantly forming them up and giving them attack orders.
If you run the game at half speed or pause the game during battles, these units can be devastating, but if you are letting the battle play out in real time, I found the amount of micromanagement they needed was not worth the effort and regularly skirmishers were just as effective from a tactical point of view with the difference being you can always order your brigade skirmishers to return to their unit and concentrate on winning the battle.
The main task of playing the Union is to destroy the enemy.
Seek to capture as many troops as possible.
Attempt to surround and destroy the entire force whenever possible.