I have a Mechromancer character focusing on the 'Best Friends Forever' and the 'Little Big Trouble' skill trees (no Anarchy from 'Ordered Chaos') that I've been playing from TVHM to UVHM with UVH Upgrade Pack Two. As long as you have gear that will supplement Gaige's Little Big Trouble skills, you should be able to do fine on UVHM.
The most important skill in the Little Big Trouble skill tree is probably 'Wires Don't Talk' (increases all Shock and Electrocute Damage that you inflict). Due to that, I use gear that focuses on taking advantage of that skill.
Instead of More Pep, focus your points into another skill. More Pep's description is misleading, as described here.
Increased Elemental Chance effects are applied multiplicatively, not additively. For example, a base 20% Burn Chance with a 30% bonus will result not in 50% Burn Chance, but in 0.2 + (0.2 * 0.3) = 26% Burn Chance.
Although, if you have a class mod that gives a bonus to More Pep, like Zapper or Legendary Catalyst, you might want to assign at least one point to the skill to get the bonuses given by that class mod.
LBT's The Stare is pretty weak (damage does not scale well) in UVHM. It also has bugs detailed here. It's pretty much a waste of a skill point. BFF's Explosive Clap seems to scale just fine in UVHM.
Gear that helps take advantage of Little Big Trouble skills:
- Zapper, preferably 'Wired' (gives most bonus damage to 'Wires Don't Talk') and blue or purple rarity (Note that the Zapper class mod's description is misleading, and due to that, the mods below are better, IMO.)
- Necromancer, preferably 'Chaotic Evil' (bonus fire rate and critical damage) and the version that gives the most damage to 'Wires Don't Talk', and blue or purple rarity. This is a TTAODK class mod. More details here.
- Legendary Catalyst (UVH Upgrade Pack Two class mod) - +5 Wires Don't Talk, +5 Evil Enchantress, +5 More Pep, +5 Electrical Burn, +5 Interspersed Outburst; bonus to Team Elemental Effect Dmg - this is probably the best class mod (and the rarest) for a Mechromancer looking to spec into the 'Little Big Trouble' tree.
An Elemental Relic (common) or a Bone of the Ancients (e-tech) that increases shock damage. The Bone of the Ancients also increases the Action Skill recharge rate, which can allow you to summon Deathtrap sooner.
- Quasar (legendary, shock-element only)
- Storm Front (legendary, shock-element only)
- Chain Lightning (legendary, shock-element only, TTAODK) - Always Shock. Regenerates grenade ammo over time. Shoots a bolt of lightning straight forward that explodes on impact and arcs to nearby targets.
Quoting Borderlands wiki:
The Chain Lightning is ideally suited for Gaige builds with heavy investment in the Little Big Trouble tree (specifically Wires Don't Talk, Electrical Burn and Myelin). Its arcing effect can also help a similar build to hit targets at range with a high Anarchy stack, as it can mitigate the accuracy penalty.
The Chain Lightning may pair exceptionally well with the Grog Nozzle, Rubi, and other Moxxi-brand weapons for health restoration. Because the damage from the grenade is practically instantaneous, health may be replenished as soon as the grenade is thrown. Adding to this end are its arcing effect to damage multiple enemies and ability to pass through some surfaces. As aim need not be precise in close- to mid-range, one throw may serve as a panic button when low on health.
- Shock 'Bouncing Bonny'
- Shock 'Crossfire'
- Magic Missile - Always slag. Grenades slowly regenerate over time. Two (Blue) or Four (Purple) child grenades home in on targets and explode instantly.
This is mostly for slagging and for helping to heal with the Rubi. I opt to go with the Magic Missile if I am playing solo or if my co-op allies don't have much slagging capabilities. Otherwise, using a shock damage-dealing grenade mod is better.
- Thunderball Fists, preferably 'Binary' (one trigger squeeze fires two shots) - deals heavy shock damage
- Little Evie, preferably 'Binary' - killing an enemy increases action skill cooldown rate by 12%; allows you to summon Deathtrap sooner.
- Florentine, preferably 'Consummate' (more damage) - a Seraph SMG that fires shock projectiles which deal bonus slag damage on impact.
Elemental weapons that have shock versions
- Rubi, preferably 'Binary' - for healing; Any damage dealt by the player while wielding the weapon heals them, at a rate of 12% of the damage inflicted. Grenades can also be used to heal with the Rubi.
- Interfacer, preferably 'Practicable' (more pellets per shot)
- Shredifier, preferably 'Rabid' or 'Ferocious' (more fire rate or damage, respectively) - deals heavy damage, eats a lot of ammo, though
- Avenger, preferably 'Hefty' (more damage) - all-around high stat SMG, regenerates bullets
FFYL weapon, or area-clearing weapons
- Shock 'Norfleet' - will deal a lot of shock damage over a wide area
- Shock 'Fibber' (second unique barrel version) - I'm putting this here, as IMO, it's too 'overkill' as a normal weapon. Quoting Borderlands wiki:
The second barrel shoots bullets that shatter upon impact or ricocheting off walls, creating pellets. It bounces off walls if it doesn't hit anything and travels with the same velocity as normal pistols' bullets. For some reason, when the shatter effect and Gaige's Close Enough skill occur at the same time, the ricocheted "homing" pellets will do 100% damage, thus ignoring the -50% bullet damage penalty from Gaige's skill...
Due to the lack of a yellow multiplier to the damage each of the 9 ricocheted bullets will receive the full bonus of amplify shields. Especially with The Bee this variant becomes one of the most powerful weapons in the game, due to the "damage per ammo"-ratio, its rate of fire and the fact, that the player doesn't need to aim properly.
- Antagonist (Seraph) - Deflects enemy bullets with increased damage toward nearby enemies. High Damage Reduction and Capacity. Launches homing balls of slag at its attackers. A good overall shield for Gaige.
Black Hole (legendary) - quoting Borderlands Wiki:
This shield can be extremely effective when used by a Mechromancer investing heavily in the Little Big Trouble tree (specifically Wires Don't Talk, Electrical Burn and Myelin) and Blood Soaked Shields. Once the shield is depleted, the singularity effect will momentarily stun most enemies in the area while pulling them in for its deadly nova blast. A single kill will then recharge the shield to full capacity, immediately readying another nova. This strategy is particularly deadly under heavy fire, where the shield will be depleted almost immediately after being recharged.
The Black Hole also makes a good shield for Deathtrap with Gaige's Sharing is Caring skill, because the singularity will pull enemies into Melee range for Deathtrap.
The Bee (legendary amplify shield) - High amp shot damage, 0 amp shot drain. Lowered shield capacity. Increased shield recharge rate. Increased recharge delay.
This increases your weapons' damage at the cost of lower defensive capability. If you find that your Mechromancer's weapons' damage are lacking, you might want to use this shield. Works best with high fire rate weapons like the Shredifier and the Avenger. The Best Friends Forever skill tree's 'Fancy Mathematics' or 'Unstoppable Force' skills, or Ordered Chaos' Blood Soaked Shields skill will help keep this shield at full capacity.