The wobbles in the arc suggest the Y axis belt(s) aren’t tight enough.
There may be a loose screw in a motor pulley, although the pulleys are often press-fit to the motor shafts. If there’s a jack shaft across the back of the machine, make sure the screws in the shaft couplers are all tight against the shaft flats.
The gantry must be square with respect to the Y axis linear bearings. If the machine has two Y-axis belts, they must be properly aligned on the drive pulleys and not off by one tooth (or more!).
The entire laser head can be loose on the X axis belt follower, so check those screws, too.
Aaaand it’s possible the screws have stripped threads or the holes are overly large.
If the lock ring holding the focus lens in place isn’t snug, the lens can rattle around inside the head.
Plenty of places to check!
Previous discussions cover those (and more!) problems:
