Boss Monster

Related: List of Bosses A Boss Monster is a type of monster that's soul will temporarily be able to exist outside of its body, after it has died. All Boss Monsters coincidentally are also bosses in Undertale. However, not all Undertale Bosses are Boss monsters.

(Spoilers Bellow.)

The game's lore specifically states two things - Boss monsters only age when their children do, therefore Asgore and Toriel do not age and are very old, as confirmed by the turtle shopkeep. Further, we know that boss monsters' souls persist after death, but not permanently. Papyrus instantly turns to dust, as does Muffet. Undyne is ambiguous due to her melting in the Genocide Path due to her being a monster imbued with great determination, but given that she knew Asgore when she was a child and he was king, it can be assumed she ages normally and thus is not a Boss Monster. In one of the ending's Alphys also refers to Toriel directly as a "furry boss monster," confirming her status further.

Sans is a confusing case. After his battle, he leaves the screen, so its not possible to see his soul and confirm that he is or not a boss monster. However, you can't hear the heartbreaking sound or when it explodes, so that could mean he doesn't have one.

To add onto this, the soul is visually represented as a "heart," as stated by Flowey at the start of the game, and only when you kill Toriel and Asgore do you see a (white) heart being shattered. No other monster has a heart appear when they die, last for a few seconds, and then break apart, as all other monsters instantly turn into dust after being killed. This is proof that the only two boss monsters - monsters whose souls persist after death for a little bit - are Toriel and Asgore.

List of Confirmed Boss Monsters

 * Toriel
 * Asgore

Monsters that are Game bosses, but not Boss Monsters

 * Papyrus
 * Undyne
 * Mettaton (He is a robot.)