Warriors and Berserkers: (Paul, Jasmine, Oleg, etc.) These tougher axe wielders often come equipped with Bows for Warriors and high criticals for Berserkers, so be a little careful of them. Speedy sword wielders can often defeat them with ease, but keep a few backup units such as Paladins to move in and save them if they almost lose.
Knights: (Bool, Yogi, Boise, Bauker, etc.) Standard procedure follows for these fellows too. Hector is the best weapon agaist them ?as he has good defense and strength, but pretty much any decent axe wielder can crush a Knight with ease.
Generals: (Lundgren, Darin, Bernard, etc.) These promoted Knights often come toting axes and lances together, making them far more dangerous then their unpromoted counterparts. Their high defense makes it nigh impossible for sword wielders to harm them without Armorslayers and the like. Use one of your own Generals or a strong axe wielder on them, but be careful.
Mercenaries: (Glass, Beyard, Puzon, etc.) These units have high skill and speed, but are generally push-overs. Almost any of your Knights, Cavaliers, and especially Paladins can mop the floor with them using a Lance.
Heroes: (Linus, etc.) Promoted Mercenaries, now carrying axes, which make them exponentially more difficult. For Linus, try to team him up quickly with Oswin ?and some other lance users while he has his Silver Blade equipped. If he has his Hand Axe equipped, team up on him with your sword users. The key is to get a one turn kill to prevent him from gaining the weapon advantage, at which point he would be devastating to your units. If you are having problems with Linus when he has an Iron Rune equipped, hit him from two sides with two FalcoKnights then hit him on the third side with the last one. Even though he has an Iron Rune equipped, your last FalcoKnight will still critical on him with her first attack.
Shamans and Druids: (Heintz, Zoldam, Teodor, etc.) Use a strong light magic unit. Plain and simple. Heintz is a push-over in Lyn's story. Zoldam may take a high critical to beat because his Luna spell is not safe for Lucius or Serra. Teodor must be killed quickly before he equips Nosferatu or else he becomes very dangerous. It's actually better to NOT use a strong light magic unit on Teodor and instead use a General or a Paladin.
Sages and Valkyries: (Aion, Sonia, Limstilla, Ursula, etc.) All of them come equipped with Bolting, a long range distance attack. Use a high speed unit or a Pegasus Knight to make them waste the spell. Aion should be relatively easy because the magic seal appears before you enter Bolting range, creating an easy kill. Then send Canas in with Luna and they are doomed. Simple as that.
Bishops: (Kenneth, etc.) Use Pent or a simply high strength unit with a Silver weapon for a one hit kill. Most Bishops besides Kenneth suck because they have low magic and usually deal 0 damage.
Swordmasters: (Lloyd, etc.) Lloyd always comes with a Light Brand, making him very deadly. Use a high resistence unit from afar and then a lance wielder up close in succession and he's done for. Other swordmasters, they fall to any good lance wielder pretty easily. If you are having problems with Lloyd when he has an Iron Rune equipped, hit him from two sides with two FalcoKnights then hit him on the third side with the last one. Even though he has an Iron Rune equipped, your last FalcoKnight will still critical on him with her first attack.
Cavaliers and Paladins: (Eagler, Erik, Damion, Eubans, Pascal Grentzer, Maxime, etc.) They tend to be terrible in Normal, just watch out because they can move fast so don't present them with any wounded targets. In Hard Mode, use high defense units, because the enemies on horseback tend to get a Strength boost.