Acquire Egbert's Egg, Sleepy Willy, and Elekk Training Collar on one character.
Peanut, Willy, and Egbert are possible quest rewards from the same quest, which can only be completed once for Children's Week . It will take you three years to earn this achievement because of the one-character restriction. This cannot be circumvented by learning it from its battle pet form - it must be learned from the item which actually "teaches" you the pet as described in the achievement tooltip.
The achievement is not part of the Children's Week meta-achievement, For the Children.