The Lord of the Rings: Adventure Card Game - Definitive Edition

By far, the easiest way to do this is the 3rd quest in the tutorial campaign, "Nuanced Concepts." You aren't given a choice of deck, but it's surprisingly easy.

Every turn, you can have one of your characters guard by pressing , then . The next attack will target a guarding character, which will also deal the damage to the attacking enemy. In that way you can destroy enemies without attacking them.

There are only 2 parts to this quest, making it a very short completion, as opposed to main story quests.

gordiedeviant makes a good suggestion in the comments: "Might be worth noting that to win the second stage, you are required to destroy the 4 'doorway' looking things that show dangers. (cobwebs, overgrown something, treacherous path etc). It's fine to attack these. Just DO NOT attack any enemies unless using the +3 Damage Gandalf card."

Hope this helps!

To earn this achievement, you cannot directly attack an enemy unit. You CAN deal damage through the guard ability and also through the ally Gandalf "Deal 3 damage" effect.
I used Quest 1 of the first campaign: Attercop, Attercop. The first 2 levels are pretty easy. Just hit the objectives ASAP. (Glint of Steel in section 1, Blocked Path -> Down a Tree in section 2)
In section 3, you have to defeat a bear boss (Kirous). In my attempt, it stopped attacking me when it had 2 health left. I summoned Gandalf and used his 3 damage option to kill the bear.
Section 4 is like 1 and 2. Hit the objective, then keep guarding and healing until you defeat 6 enemies.

Here's the deck I used:
Aragorn (Can act 2x with his power)
Arwen (heals every round)
Glorfindel (Give Gondorian Shield and guard to keep threat low)
Gathering strength x2
Unexpected Courage x2
A Watchful Peace x2
Erebor Watchmenx2
Guardian of the Citadel x2
Honeycomb x2
Longbeard Mapmaker
Secret Paths x2
Self-preservation
Wandering Took
Beorn's Hospitality x2
Imladris Minstrel (Heals when an enemy dies)
Rhovanion Outrider x2
Gondorian Shield x2
Rohirrim Lancer x2
Sarn Ford Sentry x2
Gandalf x2

Strategy: Use guard/block combo, keep threat down, resolve objectives, heal.
Good Luck!