Given the hard nature of these boss fights, just coming on top of them is enough of an awesome moment as it is relief.
Players are likely to feel especially ecstatic at beating one of the many tough optional bosses, especially the optional Rogress Mashgar, Kudoan and Allul.
Anytime your character learns a new Excel Act. Especially one that does Area of Effect damage and kill all enemies in one shot.
Special Mention goes to Niko: His first two Excel Acts consisted of a Single Target attack and a self-full heal. All the sudden he gets Niko Cannon and literally blows the enemy to smithereens!