I am stuck on both of the same hero quests. In the case of Chompzilla when I first met the quest requirements my opponent disconnected. In the case Of Grass Knuckles my opponent conceded before round 6 the first time I met the requirements of that quest.
It seems quite likely that the game has a bug where they don't want you to complete quests via concession or disconnect but they don't quite put the quest completion into the correct state.
Since those first two completions of each of those quests I have completed the quest requirements in a complete game with the correct heros multiple times and the quests will not be set to complete. It is unfortunate that it appears that this can't be fixed
