There's no need to use a deck with almost 60 cards to grind something as simple as AI3. In fact, the animation for drawing cards is probably going to be longer than your turns
I'd keep it simple and go for a non-rainbow, or a rainbow with ~30 cards.
I use this to farm Bronze Arena, but it can do AI3 pretty well, too, though you might want to even remove some cards and replace with with more "rush-like" additions. Ignore the upgraded cards, I just had them lying around:
Hover over cards for details, click for permalink
4sa 4sa 4sa 4sa 4vj 4vj 4vj 4vj 4vj 4vj 52q 55u 596 5c1 5f6 5if 5og 5og 5ur 61q 6u1 713 74a 74a 77g 77g 77g 7dm 7jv 7n7 8pm
That's the general idea. Rainbows are customizable, so experiment and see what it needs. Remember, keep it simple and clean, and aim for about 30 cards.