Here is the full list of all 28 Hatch and Slay achievements.
Kill 10000 enemies.
Survive 30 minutes in the endless level.
Use 1000 times a skill.
Survive 10 minutes in the endless level.
Open 100 eggs.
Kill 5000 enemies.
Use 500 times a skill.
Survive 5 minutes in the endless level.
Survive 1 minute in the endless level.
Survive with less than 10% health.
Open 50 eggs.
Complete the last level.
Complete all levels with 3 stars.
Use 250 times a skill.
Die against the last enemy.
Kill 1000 enemies.
Open the instruction window.
Use 100 times a skill.
Kill 500 enemies.
Open 10 eggs.
Collect 15 stars.
Use 50 times a skill.
Collect 5 stars.
Kill 100 enemies.
Use a skill for the first time.
Open your first egg.
Complete the first level.
Kill your first enemy.