Change the Symbology
Having generated your Hillshade, you will likely want to change the appearance from it’s bland gray symbology. To do this, be sure to set your original DEM layer at the top of your layers order in the Layers panel (bottom left corner of your screen). Now open up the Symbology of your DEM:
DEM → Properties → Symbology
Your symbology will vary in accordance to your own needs. If you’re looking to replicate ours, then set your Render type to Singleband pseudocolor and select the BrBG Color Ramp. Now, because we will be wanting to project our symbology onto the Hillshade layer, scroll down in symbology until you get to Color Rendering. From there, select Multiply as your Blending Mode parameter.