Heralds of the New Dawn is the third part in a series of Achievements. Each part requires players to level up a certain number of characters to Level 60. It doesn’t matter what class the characters are, or if they happen to be hardcore or softcore characters. You can mix and match as you see fit.
This series of Achievements was part of the original Diablo III game when the highest level a character could reach was Level 60. (The Reaper of Souls expansion gave players the ability to level to 70).