Magic Duels

I was able to do this with less than 10 booster packs opened, using a blue/red artificer deck. There are several cards in these colors that are synergetic with artifacts. Really though, you just want to include all your available artifacts and get them out as quickly as possible.

The achievement unlocks as soon as your fifth artifact permanent is on the battlefield - no need to win.

As an alternative to AlphaMale's solution above, the Shadows Over Innistrad update has introduced a new mechanic that makes this a breeze: Investigation.

Many of these new cards feature this ability which passively adds a "Clue" artifact to the battlefield. Simply trigger the appropriate ability five times and you're set.

Playing through the Shadows Over Innistrad campaign is actually a good way of getting this as the decks provided for each duel all feature this new mechanic to some degree (I personally unlocked it in the fifth mission).

Additionally, as pointed out by Rourc, it's possible to get the Thopter Squadron achievement at the same time as long as you have 10 untapped mana: