Mechanics of Battle
The most important thing that you should always have is balance. Try not to have too many of one type of soldier in your army like centaurs or archers. You should always have at least two wizards, one healer, one archer, one flying character and a couple centaurs. Keep the weak members of your party towards the back and the stronger ones towards the front, but don't keep the weak members too far behind or else the stronger ones will hog up all the experience. Remember to always try to build up your leader. If he's too weak then he'll die easily in battle. And if he dies then you gotta start the battle all over again.
Building Up of Levels
When a character gains 100 experience points it gains a level. Most of the time their stats don't raise much, but sometimes it raises a lot. It's very important to do plenty of what I call training battles. The point of a training battle is not to complete the battle, but to almost complete it, cast Egress, and start over so that your army grows stronger each time you repeat the battle. When a new character joins your army (all of the rookies start out at a low level), do several training battles having that character be the only one to kill enemy soldiers. Just use everyone else to weaken the enemy only to have the weak rookie hog up the killing's experience.
The Ever-so-useful Items
Each character must have at least one or two healing items in their 4 slot inventory. It's a good idea to keep one slot empty for each character because you never know when a defeated enemy will drop a rare item. Well actually you can look at an enemy's inventory, but like you're going to take the time to look at each enemy in every battle. You can't always predict what happens in battle, so when a character comes close to death, the healing items could save the day when the healer can't arrive in time. Equip the strength boosting ring and the defense boosting ring to the characters who need them most. Take advantage of special items like those that allow you to use them during battle. Be careful though, use them too much and they disappear. The only exception is the Sword of Hajya--take very good advantage of it!
The Annoying Yet Sometimes Useful Terrain
The terrain decreases the movement span of your soldiers, but it also helps defend them from enemy attacks. You don't have to worry about the effects of terrain too much. It's only annoying in the original Shining Force. Almost all of the battles take place on a nice flat surface.
Some enemy armies have a leader just like you do. And if that leader is defeated then so is the rest of his army. Its obvious who the leader is since its the only one of its kind compared to the rest of the enemy soldiers. However, I don't recommend killing off the leader unless you really have to because you could use the experience from all his enemy soldiers. Kill off enemy mages, priests, and archers as quick as you can. They can get really annoying.
Advantages and Disadvantages of Character Classes
Take advantage of your wizards when you're fighting strong enemies. Their magic always weakens the enemy with about the same amount of HP. That can be an advantage toward strong enemies, but a disadvantage toward enemies that could be easily defeated. Archers are useful throughout most of the game. The same thing goes for birdmen. Centaurs are oddly balanced characters. Some have good defense yet poor strength and some are strong yet have poor defense. Comparing this game's centaurs with other Shining Force centaurs, the ones in this one have a pretty good balance of strength and defense.
The characters that you must have in your army are Luke, Claude and Sarah. Luke is very strong and he can use healing magic. Claude is surprisingly strong in strength and defense plus he can fly. Sarah is the only healer in the game that learns the Aura spell so you just gotta have her. Characters that I highly recommend are Natasha, May, Randolf, Rhode, Higins, Gyan and Rush. The wizards I recommended are very useful for their strong spells. The fighters I recommended are all really strong in strength and defense.