Zim Number 2's history is presumably the same as our Zim's, with the noticeable difference that he is taller than our Zim and wears a hood that covers his antennae, which has a badge marked with a Z pinned on it. He also states that his greatest flaw is that he can only throw Vibrating Irken Death Blades with 99.4% accuracy, whereas the other Zims can achieve a 99.7% rate, and he greatly shames himself for that. By contrast, our Zim's reaction indicates that he can't throw them at all.
At some point prior to Issue 47, Zim Number 2 picked up an Irken distress signal coming from Pandora's Quadrangle. Following it, he was sucked through a portal to a planetoid inhabited by other Zims from other universes, and crashed, destroying his Voot Runner and his GIR. Unlike most of the other Zims, he eventually raised his rank and became part of the Zim Elite as the second most powerful Zim, only behind Zim Number 1, the ruler of the Zimvoid.
In Issue 48, he explains to our Zim (who has reached Number 100, and therefore becoming part of the Elite), how Number 1 is developing improved weapons and Voot Runners for the Elite members. When they have completed the training program, they are to be rewarded with these new tools, and sent back to their home dimensions to conquer their Earths, just like he did. Zim Number 2 also explains that the training includes intense combat, environmental navigation, worshipping of Number 1, and random combustions.
Eventually, while our Zim is struggling with the training program, Zim Number 2 states that he has already completed it himself, and is the first in line to leave the Zimvoid with brand-new technology developed by Number 1. At the same time, he also places our Zim on guard duty of the Elite's tower (which was his original job), stating that he might get his chance to leave in a few years. Zim is disgusted by having to wait and decides to steal the upgrades for himself, and leaves his security post, making the tower ripe for the Zim Resistance to break in.
After a battle of the Elite versus the Resistance, only Dib, GIR, Zim 2000 and Zim 2002 manage to continue on with the break in, with most members of both parties knocked out. The team tries to then storm Number 1's chamber, but our Zim manages to corner them using a stolen weapon.
Number 2 asks for an explanation for the massacre at the front door and Zim states that he has defeated the Resistance all by himself. He is then called by Zim Number 1 to be rewarded, and Number 2 is given the job of managing the "prisoners".
To everyone's shock, "Zim Number 1" is revealed to actually be an alternate Dib in a robotic suit. This other Dib, whom GIR quickly dubs "Zib" due to having a PAK on his head which makes him resemble Zim, explains that after defeating his Zim, he became determined to destroy all Irkens across the multiverse. Discovering the power of the Quadrangle portals, he created the distress signal to lure in the Zims, and set up the hierarchy to weed out the weaker Zims, so that the strongest ones could then be enslaved with a "Dib virus" that they would then take to the Irken Armadas of various other timelines, so they could be taken over and destroyed.
Number 2, who is the first Zim to be infected with the virus, is then sent to our Zim and Dib's timeline, where he fights his way aboard the Massive, impressing the Almighty Tallest in the process. Distracting them with rare snacks, he then takes over the ship and infects it with the virus. However, before he can go any further, our Zim uses Zib's anti-Irken weapon and the portals to alter the other Zims' timelines to make them the same as his own, causing them to disappear.
Number 2 was then presumably sent back to his own timeline, though it's unknown if he was still infected with the Dib virus.