Save up some stamina, because I'm a break down CHS like a fraction. To start, let's review basic combat.
First, always use your highest hero wearing your best hero gear (armor/jewelry). This will boost all your troop strength and defense. If you have a Rune of Fury and/or Rune of Invulnerability, they are another great way to boost troop strength and defense.
Second, each troop type is strong against one type and weak against the other. It's like Rock/Paper/Scissors.
Foot: strong to Mounted, weak to Ranged.
Ranged: strong to Foot, weak to Mounted.
Mounted: strong to Ranged, weak to Foot
If you know the defending troop types, send the troops that are strongest against them. That way you minimize troop losses.
Third, higher tier troops come with higher strength and defense levels.
T1=4 Might
T2=16 Might
T3=24 Might
T4=72 Might
T5=144 Might
That means, four T1 troops will die to every one T2 of the same troop type. The equation goes as follows: (TierLevel*Troop#)*(1+buff)=TotalMight. If your total might is greater, then you win. It's more complex than that, but basically that's it. Lowest tier troops die before higher tier troops. So, your T4 & T5 troops will all survive if you send enough T1 troops to absorb the might of the opposing army.
Now onto Campaign High Scoring...
There are basically three criteria for scoring in Campaign mode: speed of victory, number of troops sent and number of troops lost. The highest scores are done with the fewest troops sent, the fewest troops lost and use a Speed Up to finish fast. Basically, if you have T5 troops, calculate the might required to match the defending might, then send troops that are strong against the predominant troops type.
Tip 1: only send one troop type to minimize losses.
Tip 2: send only your highest tier troops
Tip 3: use a Bilbo's Hourglass to speed the combat time
Tip 4: check your combat report after each battle and see if you could've sent fewer troops, then try it again. Remember, sometimes sending more troops will achieve fewer casualties and thus a higher score. So find the sweet spot.
Now onto each campaign. I'll only post the map, the defending might and your strong troop type...
Clearing The High Pass:
1-1: 100 might, send Ranged
1-2: 120 might, send Foot
1-3: 180 might, send Foot
2-1: 1,920 might, send Mounted
2-2: 2,400 might, send Foot
2-3: 2,560 might, send Ranged
2-4: 3,240 might, send Ranged
3-1: 4,960 might, send Mounted
3-2: 4,800 might, send Foot
3-3: 5,760 might, send Ranged
3-4: 5,920 might, send Foot
3-5: 10,560 might, send Mounted
4-1: 9,480 might, send Mounted
4-2: 9,840 might, send Foot
4-3: 10,320 might, send Ranged
4-4: 11,640 might, send Ranged
4-5: 18,720 might, send Any
5-1: 24,000 might, send Ranged
5-2: 24,000 might, send Ranged
5-3: 26,400 might, send Foot
5-4: 29,760 might, send Foot
5-5: 39,840 might, send Ranged
The Necromancer
1-1: 264 might, send Any
1-2: 420 might, send Any
1-3: 600 might, send Any
2-1: 1,344 might, send Any
2-2: 1,464 might, send Any
2-3: 2,004 might, send Any
2-4: 2,880 might, send Any
3-1: 3,036 might, send Any
3-2: 3,880 might, send Any
3-3: 4,536 might, send Any
3-4: 5,712 might, send Any
4-1: 5,364 might, send Any
4-2: 6,180 might, send Any
4-3: 6,684 might, send Any
4-4: 7,272 might, send Any
4-5: 8,256 might, send Any
5-1: 7,944 might, send Any
5-2: 8,508 might, send Any
5-3: 9,072 might, send Any
5-4: 9,600 might, send Mounted
5-5: 12,768 might, send Any
Avenging Moria
1-1: 39,360 might, send Mounted
1-2: 39,360 might, send Foot
1-3: 41,280 might, send Ranged
1-4: 42,200 might, send Any
1-5: 76,800 might, send Ranged
2-1: 38,400 might, send Foot
2-2: 50,400 might, send Ranged
2-3: 60,000 might, send Foot
2-4: 67,200 might, send Ranged
2-5: 110,400 might, send Foot
3-1: 134,400 might, send Foot
3-2: 139,200 might, send Foot
3-3: 153,600 might, send Ranged
3-4: 177,600 might, send Mounted
3-5: 259,200 might, send Mounted
4-1: 254,400 might, send Foot
4-2: 264,000 might, send Foot
4-3: 254,400 might, send Mounted
4-4: 264,000 might, send Mounted
4-5: 499,200 might, send Ranged
5-1: 528,000 might, send Ranged
5-2: 576,000 might, send Mounted
5-3: 576,000 might, send Foot
5-4: 720,000 might, send Foot
Through Mirkwood
1-1: 140 might, send Foot
1-2: 180 might, send Ranged
1-3: 200 might, send Ranged
1-4: 280 might, send Ranged
2-1: 2,560 might, send Foot
2-2: 3,200 might, send Ranged
2-3: 3,840 might, send Ranged
2-4: 4,800 might, send Any
3-1: 5,120 might, send Mounted
3-2: 6,080 might, send Ranged
3-3: 7,520 might, send Foot
3-4: 9,280 might, send Foot
3-5: 12,000 might, send Mounted
4-1: 9,600 might, send Ranged
4-2: 12,000 might, send Foot
4-3: 13,200 might, send Ranged
4-4: 15,600 might, send Mounted
4-5: 21,600 might, send Any
5-1: 24,000 might, send Mounted
5-2: 31,200 might, send Foot
5-3: 36,000 might, send Ranged
5-4: 45,600 might, send Mounted
Discovering Smaug
1-1: 36,000 might, send Any
1-2: 40,800 might, send Foot
1-3: 48,000 might, send Mounted
2-1: 120,000 might, send Foot
2-2: 132,000 might, send Foot
2-3: 144,000 might, send Ranged
2-4: 720,000 might, send Any
