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