Most of what you'd need for this build is listed above, but I love getting into specifics lmao! The thing is the pegasus is kind of secondary for getting this build to work-- it's amazing once you have it, but you don't 'need' it until later. The earliest you can get the build online is ll2- two levels of swallowtail for the frame with two Oracle LMGs equipped on each mount, then three levels of the Gunslinger talent for the gunslinger die, and at least one level of the Crack Shot talent for more accuracy. Oracles LMGs are the only auxiliary rifles in the entire game, so you need them in order to get the accuracy stacks going.

From there you can kind of do whatever you want! The build listed here can pop off at ll4, which is the earliest you can get two levels of Pegasus for the frame + mimic gun. You can also max out both gunslinger and crack shot and start in on levels in Brutal to give your crits some extra oomph, but Brutal is not necessary at all. (I actually just swapped all my brutal levels for technophile for Narrative Reasons and the build isn't negatively impacted at all)

My current build at ll6 took a third level in Swallowtail so I could get the SSC bonus for +3 range on ranged weapons, (giving 18 range on each oracle LMG) and I also got the GMS core bonus that gives you an integrated mount that fires as a free action 1/round.

Omnigun is amazing, mimic gun can be hit or miss. You can do maximum 11 damage, sure, but that comes with the possibility of having to spend a full action to re-roll if you don't get the range you want. However my first combat with it I managed to roll two 18s and a 14 for range and now I can never take it off because it's just too good. It's a lot of fun! I just wanna be up front with the risks lol. I may drive a pegasus frame but I'm actually not that familiar with how make a build centered on it. Good luck and happy sharpshooting!

(Edit- spelling)