if you can keep up but struggle to get the guns to aim perfectly then that is just you learning how to use a new tool and will take some time behind the stick to sort out.
I think the tutorial in question is one where you are outfitted with gimballed lasers as the primary and seeker missiles as the secondary weapon.
Pre 1.1 this tutorial was pretty easy. You could wear their shields down as you waited for a missile lock, then fire off missiles once you got a lock. Didn't take long to take the targets down.
I bought a joystick/hotas right after 1.1 launched, and was playing the tutorials in order to train myself away from mouse/keyboard, and this tutorial is a PAIN now. Keeping the targets in your sites is a little on the challenging side, so there is that, but once you do the gimballed lasers do their little "oooh where is the target?" dance, so you have to keep them in your sites for a while before you can start shooting. And you have to get their shields down entirely with the lasers because the missiles are no help at all with that.
I thought of it as a training mission for Patience. Since I couldn't play 1.1 at all until 1.1.04 came out, I spent a lot of time in the tutorials, and it was a while before I got to the point where I could complete this particular mission in a reasonable amount of time (around 5 minutes).
I really hate gimballed lasers, that's certainly not a load out I would choose.