This one looks hard and frustrating but it's actually pretty damn easy, matter of fact, I got it without even going for it.
How? By doing the challenges. The Strategic races in the challenges menu require you to finish every circuit using only frog balloons and shield potions. You should be able to stay in first place, try the Island Of Berk track if you are having problems because that one seems the easiest and also makes it easier for the enemies to hit you.
Keep shooting the frog balloons as soon as you get them and keep activating the shields one after the other. Your opponents will fire frog balloons at you, they are like homing missiles so this is a great way to get this achievement, barely takes effort, just keep in 1st place and keep activating shield potions.