In FE9, Halberdiers are the first promoted enemy units/bosses to be fought.
In FE10, Halberdiers are the second promoted enemy class to be fought (after Thunder Sage).
The early Wyvern Knight class wears a similar helmet. Interestingly both are lance only classes with a unique skill.
In the Japanese version of Path of Radiance, Swordmasters and Berserkers didn't have critical bonuses, which might explain why Halberdiers also didn't have a critical bonus in that game.