What type of screwdriver to open this laptop?

Most PC laptops use a Phillips #00 screw, Asus is no exception. Some may use a #000, but that’s generally only reserved for things like the hard drive screws on the M.2 SSD, and even that's often #00.

The main thing to be aware of with Asus laptops is hinge screw length. The hinge scews are often long and short depending on where and getting it wrong completely breaks those screw points on the palmrest, necessitating a whole replacement part to fully restore the hinge support. This is an easy error to make if you don’t know better and you will break the palmrest 100% of the time.