Some tips to get this achievement:
1) Try to get plenty of archers in the beginning.
2) Try to get the black horse because it has more stamina than your regular horse.
3) The tricky part is to lure a deer towards your archers. First you have to rush until the deer is between your camp and you and the deer starts to run towards your camp. Then just follow the deer walking (if you rush you risk outrunning the deer so you will have to start over) until it gets killed by your archers.
If you manage to repeat it five times a day, you will get this achievement on day four.