What do Heroic and Just mean, and are there any other kinds of deaths?

No there are no other kind of death that leads God Tier’s to their eternal slumber.

To answer the other part of your question I quote Doc Scratch when Rose:

Broadly, mysteriously, and according to the case of the individual.
One may be killed by opposing a corrupt adversary and die for a just cause, as through martyrdom, for instance. This would be heroic.
Or one may be subject to corruption, and slain by a hero. This would be just.