This is what I did.
I was a norse raider so my reputation was already down the bin. I raided A LOT and saved a lot of money. I had around 100k when I tried to conquer the fortress, with a crappy army.
So I went to Northumbria, if I recall correctly around Bebbanburgh, there are many Norwegian Viking parties going around. They are "rebels" / bandits. If your army is big enough, they will run away from you. Chase them. Once you meet their leader, ask them to join you. If you are lucky, they will join for free or after some gold. If not, just leave and retry.
Hire as many Norwegian Viking as possible, they are awesome heavy infantry. Now go north. Make a permanent camp somewhere around the coast of Scotland. Now go pick your ship(s), and bring it near the pictish city you need to conquer. Now go back to the camp, pick 150 norwegian vikings leaving the rest in the camp, and go assault the city. Build the ladders as soon as possible. It might be that while you are building them, some pictish lords might assault you. I had to kill two stacks of 300/400 picts while I was sieging. If you lose too many men, simply go recruit more norwegian vikings, or take them from the camp. Now, assault the city. Your heavy infantry goes through picts like knife through butter. It shouldn't be hard to take the fortress by storm. Once you have conquered it, you should have AT LEAST 100 norwegian vikings. I've found out that 100 of them are enough to withstand an assault of over 600 pictish warriors.
Prepare for some massive battles. The picts will assault you with all they have, but their troops are no match for your chainmail wearing heavy shield using vikings. Defeat stack after stack they throw at you. If you ever lose too many troops, take the ship, go to the camp, take reinforcements and bring them back to the town. If you ever run out of supplies, run south and raid the monastery, it only takes a few hours to get there.
Overall you will have really high weekly expenses while mantaining this army. I was losing 9k each week. But I was rich, and I knew it only had to last one month. And besides, I can always make more gold if I want