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You could try assembling some kind of aggro deck in the rotation, but I'm not sure if there are enough tools available, as Shadow has limited burn and storm. In unlimited, it's easier, but aggro Shadow is still not amazing; it relies on Phantom Howl and dog units. Oil Thief isn't very expensive, in principle, but it's almost purely an unlimited deck, and crafting cards specifically for it isn't particularly great, and the deck itself is somewhat weak. There's also a reanimation strategy with the golden Ceridwen in Khavy/Mordau and Atomem, but I haven't played them yet; I'm a bit tired of it in Duels, as it's too high-variance.
Overall, in my opinion, unlimited is a great option for free-to-play players. The decks are cheap, you can swap a popular legendary for something worse but still viable, control Blood is cheaper than rotational aggro Sylvan, and so on.