I'm not sure if you really can't stand in the burning grass or not because I definitely did, you just need to be on the spot of the thing you destroyed so you'll be safe from the last hit.
And while the overall theme of the game is once again reclaiming territory from an evil dictator, there are plenty of optional activities you can engage in along the way.
If you're using a Pyro character, make sure you burn all the grass before starting the challenge to avoid getting hit by Pyro on the grass.
The turbulent waves have calmed for now.
Stay at the Edge of the Field As soon as you start the challenge, dash to the edge of the barrier.
Eventually, as the timer reaches zero, the device will prepare to unleash a final attack.