Hi c.adl!
To get into metal, you must develop a strong sense of rhythm. Lots of heavy metal/metalcore songs have riffs which you need to coordinate with timing very well. It's essential to learn how to riff and the different techniques on how to do them. It's really good that you have metal influences, they are inspirational when it comes to songwriting and making good ol' metal tunes on your guitar.
First, you can learn how to gallop. This means that you mute in really fast triplets and it's cooler sounding in comparison to single downstroke muting. Galloping can be found anywhere in a metal song, from the intro, a verse, a breakdown, even a solo. When you manage to master it, you'll be able to get creative with galloping and even do stuff like skip strings while galloping on the low E, which I personally call skip muting. You will be riffing in no time
The basic gallop can be found in the verses of Iron Maiden's The Trooper but If you do need more examples on what galloping is, you can listen to Ascendancy and Rain by Trivium, Battery and Blackened by Metallica, Room 409 and Scream Aim Fire by Bullet For My Valentine, Trashed, Lost and Strungout by Children Of Bodom...
Besides muting, adding other techniques to your riffs will be helpful in giving it character and also to make it sound hot. Techniques like tremolo picking and hammer ons and pull offs are often used. Now you can get really creative!
Now for shredding, I would really advise that you listen to the metal bands you are currently listening to. This will give you an idea on how a metal guitarist uses different scales and also the proper technique to pull 'em off.
Technique wise, you will have to first practice proper alternate picking REALLY SLOWLY. This will ensure that you will be less sloppy in your playing and you will be able to nail faster speeds if done religiously. Set some time in your practice sessions to practice your alternate picking and use a metronome to track your timing. Do not go fast if you can't, stick to your normal speed before you set your fretboard in flames. Be sure that every note you pick must ring out clearly, which requires coordination of your two hands. Also, you must learn to mute unwanted strings while you are alternate picking. Always keep the palm of your picking hand on the bridge when you are playing individual strings to prevent any unnecessary noise ringing out from other open strings.
Another shredding technique is known as sweep picking. It is when you use your pick to stroke it across multiple strings in one motion, up or down. Arpeggios, which means notes of a chord played separately, are usually executed by this technique and unlike strumming a chord it gives off a very fluid sound when being being sweep picked. My advise is to get your alternate picking right for better coordination of your two hands, then try out 3 string sweeps. Again, use a metronome and slowly sweep the arpeggios up and down with the palm of your picking hand lightly muting unwanted strings. This technique is hard, but with practice you can pull it off.
Metal is usually dark, heavy, mysterious and very middle eastern sounding. The scales which are commonly used in heavy metal would be the pentatonic minor, natural minor, harmonic minor and the exotic sounding phrygian mode. Search them up and study the patterns and then try to play them over a backing track. Over time you will start to make your own smaller riffs and solos over those scales. Over time, you will become theoretically aware of what you are playing and soon you will be shredding and sweeping really fast! It's worth the practice and that's what it's all about.
Well I hope I've helped!
Cheers