Both Uses of

immortal
in
Henry IV, Part 2

Marry, the immortal part needs a physician; but that moves not him: though that be sick, it dies not.†
Scene 2.2 *

There is your crown: And He that wears the crown immortally Long guard it yours!†
Scene 4.5

Definitions:

(1) (immortal)
living or existing forever

or:

someone famous throughout history

or:

someone who will never die -- such as a mythological god
(2) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

More rarely, "The Immortals" denotes a military corps of the Persian Empire. The Immortals were so-named because each time a member of the 10,000 man corps was killed or seriously wounded, he was replaced by another man. They are best remembered in western culture for their role in defeating the badly out-numbered Spartans at the Battle of Thermopylae.