I've been having a hard time with metalcore picking/fingering on bands like As I Lay Dying. Songs like "Through Struggle", are really hard for me to pick the palm muted low C string, and strike the non-muted G string, while keeping the clarity between the 2. It sorta just comes out muddled. I've been playing guitar my entire life, so I'm hoping it's just my inexperience with this genre. But I would love any techniques that'd help me fix this problem. Thanks!
Try anchoring your picking hand on the bridge using the meat of your palm. If you keep those strings muted in between pick strokes (and I mean immediately after pick strokes) you will have a much clearer tone.

Try watching some cover videos of the songs, and closely watch the picking hand.

Also, maybe turn down the gain a bit, it'll do loads for clarity.
1- Read the advice above
2- practice slowly , slow enough that every single note sounds right
3- listen carefully to the tone of your notes , the amount of pressure your palm is exerting on the string is essential , sometimes you just need a light touch to achieve the tone you're after , sometimes it's the other way around ...
PS : English is not my first language
One thing that I do with things that have a base low "chug" note that goes into other notes like a lot of metalcore songs and Painkiller by judas priest, is I just outside pick it. down pick all of the "chug" note, and up pick the other note. because lets face it, downpick fast or just a moderate speed is difficult to keep tight (at least for me) so doing it how I do it could be explained like speaking a sentance or a few of them. Do you just say everything without breathing or do you take a breath between every few words? Without oxygen you fall apart and have to stop the sentence, almost the same thing with doing agressive downpicking that may or may not be your level. Even if it is your level, playing it live and things like that will take a lot out of you and you'll fall apart. so think of the upstroke as your "breath" cause thats what it is, a breath for you arm muscle, i've shared this with some of my guitar playing friends, and after about 30 minutes of getting used to it, there was a big difference in their playing. hope that helps
Practice at low speed. Cross-picking and switching strings on pedal riffs can be really difficult, especially at higher speeds. Without getting used to that motion, it will always be awkward feeling.