I did this by replaying the first quest in Campaign 1 as it is not overly hard. There could be shorter quests but this was the one I used.
This quest has 4 sections that are for the most part easy to get through.
Stage 1: You can either beat the objective (8 cost) or Clear all enemies.
Since you are using Aragorn, Gimli and Legolas, defeating the enemies will be easiest and can be done in 3 turns of the first round. During your upkeep use Legolas' trigger to hit the 4 health spider. CPU will likely use that unit first to attack so use Aragorn or Legolas to attack the 2 health spiders. Once a unit of yours is hit Gimli goes to 3 attack. As long as you attack Sauron's units that haven't been exhausted, you should only suffer maybe 1 to 2 hits.
Stage 2: Objective (6 cost) required to complete. You are blocked by an objective (4 cost), you can ignore the enemies if you want.
Depending on your deck makeup may determine how fast you can get through this, it can be done without allies within 2 rounds. First round is to take out the blocked path (your heroes have enough combined to contribute by "attacking" the objective). This is where I also take time to give all heroes block and give Sting to Gimli. Second round you repeat by using your heroes to go after the objective then you activate Aragorn's power (remember to keep 1 resource available for this) to use him again on the objective to win that portion. Any leftover enemies will not be there in the next stage.
Stage 3: Defeat the boss.
This can potentially be won before the end of the first round. Legolas can hit for 1 during upkeep to take boss down to 10. With right attachments you can increase attack power to kill off the boss easy. Most likely the CPU will not have a guard unit to slow you down. If all else fails you can ready Aragorn from exhausted for 1 resource to attack again.
Stage 4: Defeat objective (7 cost) or defeat 6 enemies.
For this team it is easier to kill the enemies as many will have guard. There are 2 guard spiders right off the bat. Have Legolas hit the highest health spider. If Gimli still has Sting equipped, he can deal 4 to 5 damage to a spider due to Sting's bonus vs spiders. Once 6 enemies are defeated, quest will complete.
I would advise having equipment to give block to heroes as it will keep them alive long enough to power through. Legolas was usually the one to die on me if any ever did.