Creatures only appear in the dungeon after you've defeated them in the main campaign, so the earliest you can get this achievement is when you've reached the Ruborian Desert (there's a couple of warriors there that get added to the Dungeon).
D3cad3nce is on the money with most of the fights, add brown minions to the Arcanium sword, and green minions to the armour and you can win each fight without taking any minions. The only two to watch out for are Flamer Dwarfs and Battler Beetles. Battler Beetles can overwhelm you, so attack from one side of the arena and slowly work to the other - if you get surrounded they'll knack your health fast. For Flamer Dwarfs, I'd recommend taking five red minions into the area. They won't cause any damage, but they can't be damaged by the Flamers - use them as a distraction. Set them on one side of the arena with a guard point, the Flamers'll move towards them, or maybe just turn towards them. Dash over to the other side of the arena and start slashing at the Flamer's tanks from behind. Retreat if they start to turn towards you. Keep moving the minions so that the Flamers are always aiming at them, and it'll be over fast.
Dungeon fights are a good way to get the lifeforce achievements also - you get 75 minion points for each beetle fight.