These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Then there's the middle section riff of "Ascendancy" which is a full eight bars and filled with ridiculous accurate guitar technique and a mixed lead/rhythm approach.
Then we have "A Gunshot To The Head of Trepidation", which follows it's Breakdown-as-Verse-Riff (how did they make that work?) with this chorus: "A gunshot/ to the head of trepidation/ my promise/ if you ever lay a finger!"
Far too many moments on The Crusade to list, but this troper think the one that tops everything album is the ending title track, where there are, among other things, ridiculously arcane chords, tapping as an approach to riffing(how did they makethat work?), gleefully fucking around with tonality, and so many epic Guitar Solos that one of them happens on top the loop of Paulo Gregoletto's Bass solo!
Down From The Sky. The song centers on the bombing of Hiroshima, but that's just a context for the sheer awesomeness of the song.
Face of the Band: Not the extent of, say, Dave Mustaine, but Matt Heafy certainly fits.
Germans Love David Hasselhoff: Europe didn't really get the big first-wave metalcore explosion in the mid-00's, and for a while Trivium were huge in the UK amongst young metalheads.
Magnum Opus: Ascendancy and Shogun. Vengeance Falls is a close second.
True Art Is Angsty: Played completely straight in any song that's not about Heafy's social awareness (The Crusade) or vast knowledge of Greek Mythology (Shogun). It's pretty compelling: Heafy's definitely not a bad lyricist.
Signature Song: "Pull Harder On The Strings Of Your Martyr" and/or "Anthem (We Are The Fire)".