Talking about AMD (ATI) Graphic-Cards and how to find the right driver is a little tricky.
First lets ask what your system knows already about your Card:
lspci -nn | grep -E 'VGA|Display'
On this links you find info on AMD graphic cards and chipsets:
AMD Architecture and working driver:
|GPU architecture||Radeon cards||Open-source driver||Proprietary driver|
|GCN 4 and newer||AMDGPU||AMDGPU PRO|
|GCN 3||various||AMDGPU||Catalyst/AMDGPU PRO|
|TerraScale 2&3||HD 5000 – HD 6000||Catalyst|
|TerraScale 1||HD 2000 – HD 4000||ATI||Catalyst legacy|
|Older||X1000 and older||Not available|
Now choose the one fitting your hardware:
If your card is supported by AMDGPU install it:
sudo pacman -S xf86-video-amdgpu
If you have a hybrid GPU system with intel-amd gpu combination, get informed here: