I don't think you need to get 15 damage on one turn, just the whole round, but you can get all the damage at once if you want.
I easily got this in the fight against Cyclops when doing the Gideon Jura (Kytheon) story mode - this is the 4th battle. During the battle in which I got the achievement, the Cyclops deck played nothing that could block flying creatures. It's possible I was just lucky, but even so it made this very easy.
To get massive damage at once, wait till you have about 3-4 flying creatures and Glorious Charge in your hand. Make sure that the Armored Ascension card is on your best flying creature (+1/+1 for each Plains mana). Attack with all flying creatures on the field. Also make sure to have 2 mana set aside and Glorious Charge ready to go (+1/+1 to all creatures on turn).