How do I achieve this ceiling texture?
Many ceiling textures are created by putting some mud on the ceiling with a perpendicular motion, then swiping sideways with a trowel ("knock down"). I see some parts of your texture that look like this might be what happened.

Other parts of the texture have wide valleys with sharp narrow ridges. Those look to me like they were done very wet or runny. Maybe the mud was applied with a "normal" consistency and then knocked down using a dripping wet brush?

Usually these things are done using some combination of a trowel, an aluminum hawk, and/or a brush of some kind -- in combination with varying the consistency/thickness of the compound.

A full sheet of drywall doesn't cost a lot, especially if you can negotiate for a discount on a damaged piece. It might be worth getting a piece just to experiment on. Throw some mud on and play with it. Wait and see how it looks when dry, or if you're sure it's wrong, scrape the mud off while it's still wet and try again.