For heavy metals, aqua regia (or reversed aqua regia) followed by H2O2 works well. You just need to let fish samples sit in aqua regia in a loosely capped vial (glass or Teflon) in a fumehood for a few days. When you don't see any change in the solution anymore, you can add a small amount of H2O2 to enhance the digestion. Add H2O2 in drops and swirl the solution because H2O2 reacts intensively. Only add H2O2 when the aqua regia digestion is almost complete. You only need a fumehood, vials, acids and H2O2 in this method, but you need to choose the type of vials and the grade of reagents based on the concentration level of metals you are dealing with. For trace metal level, you need to use Teflon vials and trace metal grade acids, which are not always cost effective. The digestion process can take one or two weeks to complete, but does not involve a lot of work. Once the digestion starts, you just need to check the progress once a day.
You can find a lot of other digestion methods in literature. EPA also has recommended digestion method for heavy metals like Hg.
You can ash your samples using furnace if your lab have one, followed with concentrated HNO3 digestion of the ash. Filter the solution and top up to your desired volume. Run AAS after that. Feel free to refer to my paper.