From RWP Wiki
Blue Eggs are items in the Banjo-Kazooie series.
Blue Eggs are the basic variety of projectile Eggs. They can be shot out as an attack or dropped to fill something up.
In the Games
In Banjo-Kazooie, the ability to use Blue Eggs is taught by Bottles in Mumbo's Mountain. At first, Banjo and Kazooie can carry up to 100 of them, but with the use of a Cheato code, they can carry up to 200. In the room just before the final battle with Gruntilda, there is a large Blue Egg behind a Note Door that fills up their current total to its maximum.
In Banjo-Tooie, many new abilities take advantage of Eggs. The ability to fire them in first-person view, under water, in the air, to fire other varieties of Eggs and even to fire them while holding Kazooie like a gun are added. In this game, Blue Eggs are the weakest variety, doing 1 damage to bosses.
In the first-person shooter sections of Banjo-Tooie, such as Targitzan's Temple, an item called the rapid-fire egg could be picked up, allowing Kazooie to shoot eggs non-stop as long as the player holds the fire button.
Banjo-Kazooie: Nuts & Bolts
In Banjo-Kazooie: Nuts & Bolts, Blue Eggs make a minor appearance. While Banjo and Kazooie have not retained their previous moves in the eight-year gap between Tooie and this game, the Egg Gun and Egg Turret vehicle parts allow the duo to fire Blue Eggs once more.