Okay, for everyone who needs a bit of help with this, here is what I play.
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The immortals add a bit of damage and can get under the Gravity Shield, The Lobotomizers draw permanent control cards, so they act as a buffer for your shield as well as adding a bit of damage.
If you want to upgrade for more efficiency, do so in this order: Dimensional Shields, Pillars, Immortals, Lobotomizers, Dragons
I have 4 Phase shields in my deck, and that one quanta can be the difference between winning and losing.
When playing this deck you want to wait a while before playing any shields. Each turn of small hits you take will save you a turn of bigger hits later in the game. You shouldn't expect or try for a mastery with this deck. I try not to get below half health, or more than 4 points of poison on myself. This way you have enough health to survive some direct damage. Most of the time I have around 17-19 cards left in my deck when I play my first shield. This means that I should have about enough shields to last me the rest of the game. (3 turns of protection times 6 Shield equals 18 turns of protection) Once you put out a shield, keep them up for the remainder of the game. Only use the Lobotomizer against creatures that can make you lose such as Momentum, Destroy, Light creatures when Hope is out, Mitosis (which has synergy with Empathic Bond), etc. As far as getting creatures out goes, its always worth waiting the extra turn to put out a dragon rather than an Immortal.
There are a lot of ways this deck can lose, but don't get discouraged. The point is to grind out lots of games to get as many spins for upgraded cards as possible. Finally as a word of advice, don't quit a game because of the AI's shield. The AI is dumb and will cast a bad shield over top of good ones giving you a chance to win.