So what I would consider the most closely related tool to an air hammer is a hammer drill. The one I would look into first would be the Dewalt rotary hammer drill. It comes from a high-quality brand and has a solid warranty.
So how can you make this work?
You can buy the hammer drill, and then also buy a chisel bit separately (here is a good one) to get that air hammer-like function for blasting through concrete, brick, and various other materials. The Dewalt rotary hammer drill is slightly pricey, but overall less expensive than buying an air compressor and air hammer combo, which could run upwards of $300+.
The nice thing about this hammer drill also is that you have two choices in size. You can choose the one inch or the one 1/8 inch, depending on the needs of your project. The 1 and 1/8 in is about 20 bucks more so It might not be worth it if you’re looking to save as much money as possible.