The description of this achievement is misleading as you don't need to do it in a single picnic battle.
You can do this while in one of the world hubs (place where you do the races, time trials etc)
So once in a hub you will need to find each of the 4 power ups Iguana, Owl, fish & Bee, if all 4 aren't in the hub then quit out and come back in.
Once you find all 4 you will need to use each of them, they are as follows...
Iguana = Shield
Iguana + Iguana = Chicken
Owl = Speed boost
Owl + Owl = Mortar strike (needed for the OUCH achievement)
Fish = Double rockets
Fish + Fish = 5 Rockets
Bee = Bee's nest
Bee + Bee = Mushrooms
You just have to activate each combo for the achievement to unlock.