Two knights, a Priest and Pegasus Knight and I'm done in one turn... any help?

I am going to guess that I am doing everything wrong and really need some tips.

Disiciples 2?
Depends on the enemy, but I wouldn't take 2 knights with my pegasus knight if your party size is restricted to 4 units. Rather take one knight and either two healers or one healer + an apprentice. I would go for the latter though since it can be dangerous not to have any magic attack units in your party as some units are totally immune to physical attacks, such as the werewolves which are encountered in the empire saga.
Also, consider buffing your own units with defensive spells and softening up some difficult mobs with magic attacks or magic summons. The spell "magic armour" works wonders in this regard. Usually it can unload at least two attacks on a front line target before it gets killed. Then you can quickly get rid of that unit when you attack with your main party :D

If you're being wiped in the first round of battle i'd bet you hit the enemy capitol. Just like yours it has a near unbeatable unit guarding it, having an AE attack, very high initiative, and a ton of hitpoints. If it's not the capitol guardian then maybe you just had horrible luck on all initiative rolls, load a save and give it another go.

Try to soften up your target first with summons or other units. Have them gather at the gates and then attack on the same turn. This way the boss units have a smaller opportunity to heal back up. It doesn't matter the strength of them of your other units just that they are able to cause damage to one target. Better a unit with lesser hit points. Once they die they stay dead. It makes it a little easier for your main force then to achieve victory if your having a particularly difficult time with a boss.

If you have plenty of gold, bring along a few green hero squads to soften the enemy up. But it won't work at all if they don't get a chance to damage the enemy, so you would have to figure out a solution to that problem first.... you may have to wait for some spell or loot that might do the trick.