Well, if you want to beat dimensional shield specifically, there's a few possibilities:
-Poison. Creatures and Arsenic will be blocked by the shield, but if they can get some poison on the opponent first, it will continue to damage them. Also, the cards Poison and Chrysaora (and upped versions) will work even if they have a shield up.
-Permanent removal. Deflagration, steal, pulverizer, or butterfly effect. (or a very lucky mutant) Any of these will destroy the shield.
-Momentum. Titan, Sapphire Charger, and the card Momentum will get you through any shield
-Direct Damage. Fire bolts, Ice bolts, Drain Life, etc, will hurt any opponent unless they have emerald or mirror shield. The disadvantage is that these don't do a lot of damage, so you'll either need a ton of quanta/bolt cards, or you'll need to do some serious damage in another way, and just rely on these as a finisher.
Another trick you could do is use a deck something like ninetyfools posted, where you simply try to stay alive long enough that you can outwait all of the dimensional shields. A deck with breeding cards like mitosis, firefly queen, or pharaoh, and then empathic bonds can keep you alive for some time if you get set up right.
I have a fully upgraded poison deck that works extremely well in bronze, but I don't really think it would work well unupped. Permanent removal, particularly pulverizer, is an excellent option. I haven't tried the other options I suggested to farm bronze, but done right, I think they have a good chance against monoaether.
