Staggering is an incredibly important part of Dauntless because it provides windows of opportunity to weaken a Behemoth, and deal massive damage to them while they're downed. While all weapons can cause Stagger, the Hammer causes the highest amount of Stagger Damage (that's the blue damage against a Behemoth, not the yellow or grey). 

Each Behemoth has an invisible Stagger bar, and simply put, the more Stagger damage you deal, the quicker the enemy Behemoth will falter and fall. Dealing damage to a Behemoth's legs deals 50% Stagger damage, and the head 100%. Try to aim for the head, with Behemoth's who're weak indicating their soon-to-be Staggered status by a white fuzzy animation around them. Continued strikes against the head (or legs) will then cause a Stagger.

Finally, the Weighted Crown modification as a Hammer user will allow you to deal full Stagger damage to legs, reducing the need to constantly hit your enemies skull. Xploit has a great video on the below.