This is very simple to unlock.
When you start the game on level 1, there a total of seven crystals to collect (which look like emeralds)
Collecting your first one will earn you:
collect another four to earn this achievement.
As reported in the Xbox Achievements forums (and confirmed by Shinnizle), you can play level 1 three different times to get the other achievements (Credit goes to bLaKgRaVy for this.)
https://www.xboxachievements.com/forum/topic/484388-mushroom...