use the payload cart to help shield yourself from his flame attack. Does not totally shield you but can be used to close in or aid in escape.

Use the totem legendary to give your green circle cc immunity. Deploy to heal and hop inside when the grumpy bomb is near you. Grumpy bomb does little damage so the totem essentially negates it.

take out the turrets. nearly all good Barik players use the card that lets them gain healing from there turrets

It is possible to stun him and kill him in ancient rage. So any crowd control ability can pin him allowing you to either move away or let the team focus damage on him.