It could be the rubber shock mount bushings, instead of the shock, itself. You might try spraying the rubber bushings with silicone spray. I don't know for sure if that will fix the problem, but it's worth a try. You can get silicone spray at your local auto parts store. A lot of people will tell you to use WD-40 on rubber bushings, but really, you're not supposed to. You're supposed to use silicone on rubber bushings or rubber mounts. WD-40 can cause the rubber to dry rot.
Agree^^^ I'm going to lay a bet on the A-arm bushings instead and the ball joints.. Late model ford truck and suvs were notorious for the front end squeak which was the lower ball joints you can drill a tiny hole in them and tap it for a zerk fitting and you will have geaseable joinst the I've done it before on cars.
I am working on a friends TRX 350 ES Rancher with a similar problem. I have not ridden the machine, but I grabbed the lower "A" arm and it flopped a bit so I figured the bushing/rubber was bad. It is soft so I ordered the "A" arm, but now the frame mounting boss and the bolts are worn as well. This allows the "A" arm to move radical distance at the axle.
I will try to repair with a bushing/washer of some type unless there is another fix I am not aware of. Pretty thin to weld on, and the holes are oblong at this point.
While under there I found that the left shock has come apart. So many problems on the left side at the same point it is hard to tell what actually caused the original problem. The "A" Arm alone is not going to fix the problem. Any ideas???