The Baby Maker seems like "a must have" especially if you wanna do Hyperius quite easy. Just start farming for a gun :)
I think you gotta have some other really good gear if you gonna half his health before his minions are summoned.
The Tediore relic would help. I did it with two baby makers gunzerking and skill points for extra magazine size, still I only got his health down to half. I did not have the relic though.