This is unlocked on the 4th mission of the second Anglo-Saxons campaign, "Harold II Godwinson".
I managed to do this on normal at 4 minutes and 20 seconds using the following method:
At the beginning of the level, quickly gather your troops and send them to the base, gathering the surrounding resources (there should be 4). Then, build a house and as soon as it's done, build a Spear Guards unit. When they're done building, you're ready to set out. For reference, I was at about 1 minute 25 when I set out.
To the right of the base will be a bridge, with an enemy berserker on it. Avoid him at all costs. Instead, you can go a little north of the bridge to cross the river. Some archers spotted me doing this, but it didn't matter in the end. Once you cross the river, there'll be a spy trying to run away, you can't miss him. Take him out, then proceed towards Haralds camp on the far east side of the map.
He will send a couple of level 5 units to stop you. I previously tried to use a single unit to hold them off and that ended up biting me in the ass, so take them on. Now, it is extremely important that you keep Dunstan out of melee combat! You need him healthy as only he can take out Harald. Fight through Haralds units until you're close enough to aggro him with Dunstan, then make sure Harald enters melee combat with your warriors and NOT Dunstan.
When that is all set up, keep Dunstan firing arrows at Harald, remembering to use his "Sharpshooting" ability. With any luck, your soldiers will be able to hang on long enough for Dunstan to take out Harald. I certainly cut it pretty close. The achievement should unlock as soon as Harald is dead.
Also, remember to retreat your other hero when he is close to death, as the mission will fail upon his death.
You may want to skip cutscenes just to be safe. I'm not sure if the clock stops during them, but better safe than sorry.
I was able to replicate my method on easy and clocked in at 3 minutes 55 seconds, so that is definitely the way to go.