It definitely sounds like you are ready for the non-apprentice mode of the game.
Grizzlies have tremendous amount of health, armor and damage, but it is a single big creature. Control spells such as Force Hold and Turn to Stone can totally neutralize it. So can stuns and dazes.
Like any nonflying "big", a flyer-heavy deck can simply ignore the Grizz and swarm overhead.
Compared to other "bigs" the Grizzly is relatively vulnerable to swarms, as it doesn't have Sweeping or Counterstrike or Vampiric. While 3 Armor will soak a lot of damage, it can at most kill one weak creature per round, and if it rolls badly and fails to kill one its round is essentially wasted.
Also like all "bigs" the Grizzly doesn't actually hit that hard compared to an equivalent-cost swarm. The Grizz costs as much as 4 goblin grunts, or 4 ring of beasts bitterwood foxes, but either of the 4-creature swarms can roll 12 dice (3x4). Depending on your tactical situation you may be better off ignoring the Grizzly and going straight for the Mage. (the same cannot be said for swarms, swarms do too much damage to ignore)