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