How do you fight back against unfair trade practices of other countries if you do not use tariffs?
The only unfair trade practices that the US needs to address involve the theft of proprietary property. That's one of the main reasons the WTO was established. Almost without fail China has abided by rulings from the WTO.
The other unfair trade practices that get bandied about include a foreign government subsidizing one of its companies to give that company a competitive edge in pricing, and tariffs one country places on another.
So let's look at those one at a time.
A government gets the money to subsidize a politically favored company by taxing its citizens. It takes from its "Joe Sixpacks" and gives it to a politically connected company, which then exports its product to another country and is able to charge lower prices. In other words the South Korean "Joe Sixpacks," for example, are paying a portion of the bill when an American buys one of the subsidized products, say a new washer/dryer. When you understand that you realize the unfair trade practice is actually directed at the taxpayers of the subsidizing government, not the consumers from the country buying the product. So the appropriate solution for the consuming country's government is to do nothing. Maybe cheer them on, because it realizes the bargain its consumers are getting.
As has been discussed ad nauseam on this board a tariff is a tax on the consumers of the country imposing it. It is a hidden tax, if you will, on a government's own citizens. Like with subsidies the appropriate response is to do nothing. Responding with tariffs of your own does nothing but tax your own citizens. It's telling the other country: "Oh, yeah! We'll show you! We'll harm our citizens just as much as you harm yours! That'll show ya!"