Mystery Pink Egg:

To find the location of the mysterious Pink Egg
from Banjo-Kazooie, go back to Spiral Mountain. 
Just above the tree stumps where the speed shoes
are located is a hole. In the hole are metal bars
enclosing in a Banjo-Kazooie Game Pak. To destroy
the metal bars, you will have to learn about 
Grenade Eggs. Use them to blow up the bars. Go up
to Gruntilda's Lair to find a Flight Pad so you 
can fly to the hole and break open the Game Pak 
to find the Pink Egg.

Mystery Blue Egg:

Go back to Spiral Mountain and use the Flight Pad
to fly up to a waterfall with a hole in it. Jump 
all the way through the rushing current to find 
the Game Pak. Use the Grip Grab skill to break 
open the bars.