This is a suggested guide for Gaige players tackling Digistruct Peak. From the title you can see I favor a particular weapon- I’m not saying you need to favor it but since I play with a couple of restrictions it’s what I featured 
As with my Krieg Peak build & guide I don’t reset the game to get quest rewards and I rarely use RL. Also, I have to point out that I do use a 25% BAR for the purist among you. Here’s a screenshot of her build:
http://bl2skills.com/mechromancer.html#550020110000350025150510413150151050
This build can accommodate all of Gaigge’s legendary coms except the L. Roboteer and only misses 20% Cooler on the L. Mechromancer. As for the load out:
Weapons:
Elemental Infinity- shock and corrosive mainly
Slagga- Bulets Go Fasterifed if you can but really any version will do
DPUH- my FFL/boss weapon of choice
GN- insta-heal + insta-shield goes a long ways towards staying alive with such a fragile shield. Multi pellet shottys and AR are also a good choice and having an Avenger to regen SMG ammo is a plus. You could even find a use for the Storm as well…
Shield/s:
The Bee- use the one with the highest amp damage- bonus if it has immunity. For the most part no need to worry about shield recharge with BSS. This will be used for the majority of the Peak except where specifically noted.
Grenades:
Storm Front- Longbow or Homing
Chain Lightning
MMx2 or x4- for when your SMG ammo might be low (like when you decide to use a SMG along the Slagga)
Pandemic- Longbow or Homing- great for constructors.
Fastball- Anarchy doesn’t work with grenades but damn if it isn’t an effective weapon just the same…
Class mod:
In order to use the Infinity with a LBT/OC build you’ll need a Neutral Necromancer com from the Tiny Tina dlc- Queen Scream is wearing a Chaotic Neutral Necromancer with +50% mag size, +34% fire rate and +5/+3/+4 to MoSS/So5G/WDT.
Relic:
Shock BotA 99% of the time, Sheriff’s & Deputy’s Badge depending on the enemies involved.
Up until OP4 Gaige should be able to handle the Peak pretty much like everyone else but once you get there you might want to adopt these suggestions:
Dual Scorches- Gaige shouldn’t have trouble with Scorch until you start to get the twin Scorches and/or twin Scorches + surveyors. Again, the key to this to restrict the direction they can attack you- lure them back to the prior area and use the gateway there as a bottleneck. Use all available Storm Fronts and watch them fry. Try to lure the surveyors away to deal with them one at a time- don’t release DT too early or he may attract the Scorches as well- you only want to get the surveyors following you. Once they do you can unleash DT then.
Dukino’s Mom- use DT to keep her distracted although you may want to go with a beefier shield if there aren’t any spawns at this particular OP level. This fight is all about NOT taking damage- her shock balls can kill even the strongest shields and with no minions you want to take as little damage as possible. Blockade or your best adaptive shield if you have them and unless you get the spacing right to where she doesn’t attack go with your best corrosive or highest DPS weapon if you have high Anarchy stacks.
Black Queens- pretty much the same as the Scorches- lure to archway, saturate with slag and Storm Front the bejesus out of them, using your weapon to help the battle along.
Train turrets (and turrets in general)- DT for the distraction and Pandemic or Storm Fronts for the assist, making sure to apply slag via the Slagga liberally (and with enough stacks the Slagga becomes its own very efficient killing tool).
Doc Mercy + constructors- target the Doc first and try to keep DT in your pocket for as long as possible. Try to keep the constructor’s turret alive for second winds if needed and don’t be afraid to switch to a beefier shield if things get hairy-a Blockade, Antagonist or adaptive shield if you have them. You might also want to change your com and relic as well- either the L. Anarchist or L. Catalyst with the Sheriff’s Badge.
Assassins- definitely switch shields for this fight when you get the x4 spawn (something I learned after a few respawns). Keep moving and use DT as a distraction- so long as you break their line of sight you can try to use Close Enough and The Nth Degree to your advantage- spray, pray and run like hell! To this end you may want to have a singularity grenade on hand.
Saturn- stay behind cover and try not to bother with DT as he won’t be worth it. Eventually your InfiniBee should win the day 
OMGWTH- DT sticks while you move- unless you’re feeling VERY confident switch to a beefier shield and your heaviest hitting guns- DPUH (unless you saved certain quest rewards until later) + Sheriff’s Badge is pretty much what I’d go for.
General tips:
I like shotguns with Gaige so if you have any favorites go ahead and include them in your backpack- elemental CC can be killer. Don’t underestimate the Dahlminator for Gaige vs constructors- thanks to their semi-homing nature you can practically shoot around corners and hit your target. Other weapons of use would be the Hail vs turrets/constructors, the Hornet vs surveyors and Verucs- their spread pattern makes them very effective against large targets and even surveyors. Using the Bee means target prioritization becomes paramount- UBA slag skags, UBA surveyors, UBA psychos and rabid skags should always be targeted/tracked first. DOT damage can be fatal while wearing the Bee- do what you can to take out fire loaders, fire spiderants and foes with corrosive weapons first and fast. The Transformer shield is a boon when dealing with enemies using shock weapons (it won’t help much vs Dukino’s Mom thought).
So that’s it-probably not the most efficient choice of weapons but if you’re like me and always worry about running out of ammo at the wrong time (as there’s never a right time to run out of ammo) I hope this can offer you enough to get your Gaige to OP8. Good luck! 