The devs have said the effect can drop from any gamemode except AI duels. Though to be honest, I've tried both PvAI Brawls and Dominions without a single drop, but I've gotten almost 1 drop every time from the Event game mode, so I'd actually suggest just farming that.
Keep in mind you have a chance to loot both the effect, or a Battle Outfit for any of the 16 heroes, and the Effect only counts for 1 category, e.g. Idle, Execution etc. So you might be in for a long grind.