What Metallica was using to record that album was a Marshall Plexi with Tubescreamers stacked in front of it with 4x12 cabinets. You're not going to get that sort of sound unless you get a Marshall Plexi and shove Tubescreamers in front of it and at the very least, get a guitar with humbuckers in it. You'll also need to be able to play like Metallica do as well which is something that only the band can do as well.

That sounds unhelpful, but it illustrates the point that with only an amp like a tiny little Fender G-Dec, you're going to need to control your expectations. Your guitar only has single coil pickups too, when what you really need for that sort of sound is a guitar with humbuckers. If you want to sound anything like Metallica, you're going to need an entirely different rig.
Roses are red
Violets are blue
Omae wa mou

Quote by Axelfox
Yeah, you'll really want a guitar with humbuckers, a Marshall type amp, and a closed back speaker cabinet.
Tough crowd tonight. . . These guys are correct but it's not really helping you.

For what you have try the Metal or HotRod setting. Tone a bit to the right of 12 O'clock. Gain around 3 O'Clock. Use your bridge and middle pickup together for a humbuckerish type of tone. I'm guessing on your amp knobs, I just looked at the picture. And put your amp against a wall so that the wall acts as the closed back and point the speaker at your head, you don't have ears on your knees.

If you want to spend more money then you have some options. The cheapest of which is a Distortion pedal and then run your amp on the cleanest setting it has. If you don't have much $, try the Joyo JF-32 Hot Plexi and maybe run a Joyo Vintage Overdrive in front of it (guessing here, never stacked them).

There are tons and tons of other options. It all comes down to budget, how loud you can play, and if you have a place to put everything.
Ibanez RG1570 Prestige
Jackson Kelly KE3 - MIJ (Distortion/Jazz)
Jackson DKMGT Dinky (EMG 81/85)
ESP E-II Eclipse Custom (JB/'59)
ESP LTD EC-1001FR (EMG 81/60)
Fender MIM Strat

Mesa/Boogie Dual Rectifier Roadster 212
Laney IronHeart IRT-Studio
Peavey Vypyr 30
Peavey ReValver Amp Sims
TOOOO many T.C. Electronic Pedals. . .