Pretty neat game! To split the game into its two parts:
I wish the collecting of eggs felt a bit more interesting. Maybe if there were enemies lurking around, or you had to do a small minigame with collecting them, or they'd break. Something to spice it up a bit more. Also, delivering a story or purpose in collecting the eggs would give the player more motivation to collect them.
For the boss battle, this is probably the most fun part of the game. Increasing the number of boss fights you do, or giving the boss battle a lot more substance in terms of time and complexity in difficulty (maybe you have two circles appearing simultaneously) would make it feel a lot more fun and engaging.
Really nice job though! Played till the end!