For Apex there is timed acceleration built into the game that cannot be entirely overcome, but you can use custom mouse curves to mitigate it as much as possible. The aim/look speed of the game isn't too bad overall, so I suggest finding a mouse sensitivity that feels good and allows tracking your shots well while shooting enemies in your field of view, then using a curve to increase the turning speed for enemies behind you. The hardest part is dialing in the curve for turning around. I would start with one of our sample profiles and dial it in for you.
I've attached a couple additional profiles I've been playing with for you to tryout.
XB1 Apex Legends 5-30-19.profile
XB1 Apex Legends 6-7-19.profile