I'll suggest these:
Akira
Another
Attack on Titan (jap. Shingeki no Kyojin)
Berserk
Bleach
Boruto: Naruto Next Generations
Btooom!
Corpse Party: Tortured Souls
Danganronpa: Kibou no Gakuen to Zetsubou no Koukousei - The Animation
Danganronpa 3
Deadman Wonderland
Dragon Ball Super
Elfen Lied
Fate/Zero
Future Diary (jap. Mirai Nikki)
Hellsing
Highschool of the Dead
Higurashi no naku koro ni
Naruto
Naruto Shippuuden
Shiki
Soul Eater
Steins;Gate
Tokyo Ghoul
Umineko no Naku Koro ni
Deadman Wonderland, Btooom!, and Tokyo Ghoul just barely missed my list of favorites. And of course Shingeki no Kyojin! Can't believe I forgot that one. Good suggestions, I will use this as a reference after I binge watch DBZ Super.
I wouldn't bother with Boruto. It's essentially fanfiction of Naruto where all of the old characters do nothing. You also listed a lot of shows that I'd consider suitable for 13-15 year olds, like Elfen Lied, Future Diary, Deadman Wonderland, etc, but aren't appropriate for an older crowd.
Berserk is a better choice for the older crowd.