Here is the full list of all 34 Kingdom: Classic achievements. It takes around 20-25 hours to unlock all of the achievements on Windows.
Survive past day 25
Survive past day 20
Survive past day 15
Survive past day 10
Survive past day 5.
Recruit 8 archers on the first day.
Get free walls on the second day.
Do not start your camp until day 3.
Hunt 20 deer before the end of day four.
Kill nothing until day six.
Have more gold than you can carry by day six.
A nimble ruler will never let his money touch the ground.
Do not let your steed run away before this day.
Destroy by this day from whence they came!
Survive past day 30
Survive past day 35
Survive past day 40
Survive past day 45
Survive past day 50
Survive past day 55
Survive past day 60
Survive past day 65
Survive past day 70
Survive past day 75
Survive past day 80
Survive past day 85
Survive past day 90
Survive past day 95
Survive past day 100
Clear an acre of land before the end of day seven.
Secure the crown by making your kingdom safe from harm.