Hearthpwn

I do not have Alexstrasza so I had some serious difficulty defeating Heroic Grobbulus. After a lot of trial and error I found this strategy to be very effective and inexpensive. It will be a close fight, but this deck can definitely help you defeat him. If this deck actually helps you defeat Heroic Grobbulus, please upvote! Enjoy!

General Overview

They key to defeating Grobbulus is to use his hero power against him, as with every heroic boss. Since he does two damage at the start of every round, what kind of minions or spells benefit from this? Enrage minions. Combo these minions with Power Word: Shield and they are more likely to survive a few rounds. Once your minions have utilized their rage, AOE heals like Holy Nova and Circle of Healing are able to ready you to rinse and repeat. This is VERY IMPORTANT: make sure you attack before you heal, otherwise you will lose the benefits of enrage!!

Lightwell's are unpredictable and can get in the way, but that +3 healing has saved my life more times than I can count. The Injured Blademaster can give you the damage needed to eventually kill Globbulus as well. Combo this card with Divine Spirit and Inner Fire for added damage. This combo can also work with Sen'jin Shieldmasta and Stoneskin Gargoyle depending on which show up together. 

Shadow Word: Pain and Shadow Word: Death are your two main removes while Holy Nova is as close to a board clear as you get but if you can combo this with killing an Abomination of his, this becomes very effective. Healing is extremely important in this deck: if you cannot keep your minions and yourself alive then, you cannot beat Grobbulus. I have won while being fatigued with this deck, sometimes it gets that close!

When making trades always remember to leave your minions with more than 2hp or let them die BEFORE his turn, otherwise you give him an extra 2/2. Always plan out your attacks and mana before making your move.

Mulligan

We are always aiming to get the Northshire Cleric in the opening hand along with a Shadow Word: Pain. A Tauren Warrior is also a welcome sight in the opening hand or a Holy Smite. These low level cards will keep you going until you can get a Lightwell or Nerubian Egg out quickly.