The easiest trick to solo Hyperius is to use the Evil Masher Glitch/Exploit. It hasn't been patched yet, but it's been around a long time. Basically, the Evil Masher is an assault rifle with sub-par stats, a reward from Marcus's mission (Kai).
When reloading however, there is a chance to "power up" the weapon. Taken from the BL Wikia:
There are at least six possible outcomes to Evil Smasher reloading:
Power up level 1, indicated by the power-up sound and explosion. Slight increase in power and reduced recoil for bullets in the next
clip. No change in clip size.
Power up level 2, indicated by a louder power-up sound cue, and explosion larger than that of level 1. All round improved weapon stats
compared with level 1. In particular next clip increases in size to
about 30.
Power up level 3, louder cues than level 2, high stats than level 2, in particular clip size increases to about 50.
Power up level 4, the previous trend continues. All round improvement to level 3, in particular clip size increases to about 70.
Power up level 5, similar as before but bigger and better. In particular clip size increases to about 90.
Nothing. No sound or explosion. Weapon returns to base stats for the next clip.
As for the glitch:
As soon as the power-up sound and visual cue occur on Evil Smasher,
and if player swap Evil Smasher right away, the power-up effects of
Evil Smasher will now apply to the newly swapped weapon, and stacks on
top of the weapon's other properties. ALL weapons in active slots now
inherit ALL of Evil Smasher's special property of powering up (i.e.
chance to power-up after reload, with same explosion and power-up
sound).
Take this example. Say when reloading Evil Smasher, the cues indicate
the next clip with be at the highest power-up level. If the player
switches immediately to, say, Infinity, before Evil Smasher finishes
reloading, Infinity now has increased clip size, improved damage, fire
rate and recoil reduction proportional to Evil Smasher highest
power-up level. Even though the normal Infinity property of having
clip size of 1 is "overwritten" by Evil Smasher power-up, Infinity's
other original properties (never using ammo and bullet spread looks
like infinity symbol) remain.
When combined with the Infinity repeater pistol in the stated manner
and The Bee, and due to the dramatical increase to fire rate, the
player can kill any of the Invincible foes in a matter of seconds
(usually less than five seconds, even on True Vault Hunter Mode). For
example, Voracidous the Invincible can be killed before Chief Ngwatu
spawns, and Hyperius the Invincible even before his loader minions
have time to make it invulnerable. This exploit has, as such, game
breaking effects. Also, when using this glitch with Voracidous, he
will instantly respawn after going outside of the fightning area,
without the need to pay Eridium again or rezone.
This power-up effect applies to all weapons in active slots until the
current game session ends, or switching back to Evil Smasher. It does
not go away even after respawn, fast travel or entering inventory
menu. In multiplayer session, the clip count may reset to base stat
after fast travel, still all Evil Smasher properties remain.
This glitch is most noticeable for weapons with low clip count, such
as Rocket Launcher and Sniper Rifle. Rocket Launcher under this glitch
can easily have clip size above 27, more than the maximum a normal
backpack can hold
