There is a huge problem that World of Warcraft also had. Some quests asks you to kill a certain named enemy, however, a lot of players are waiting for the boss to spawn and kill it too quickly for everyone to complete the quests. There are also players who will do AOE attacks and the enemy/mini boss would die instantly.
My idea to fix it is to scale the mini boss to the amount of players in the area, so even if there are 20 players, the Elite will still pose a small challenge and not be defeated in literally one second.