In the Smash Bros. series, Peach performs the attack by hitting her opponent with her rear. Upon impact, there is an explosion of hearts (an explosion of fire in Melee).
In Super Mario Dream, Peach performs the attack very similarly to how she does in the Smash Bros. series. Sometimes, however, she may not use her rear to attack. In some episodes, Peach may perform Peach Bomber by simply tackling her opponent while facing forward instead of using her rear.