Buzz Axe Rampage : Because, uhm, well, I like to have the skill, and be able to spend my skill points.


The starting of all the fun (And explosions)

Empty the rage: This increases melee damage, and increases it even more when the shield is depleted.
"A broken shield is a good shield."


Embrace the Pain: Shield's increased recharge delay helps roids shields, and the extra fire rate benefits a lot from the Rough Rider.
"Sorry, I get nervous with my shield down."


Thrill of the Kill [1/5]: I started with 5 points on this, then 3, and then 1, and even with only one, a melee kill is enough to restore almost (If not all) our health while not in rampage.
"You have too much life, give me some"


Strip the Flesh: This increases explosive damage, and this means bigger bloodsplosions, and more death, and you know, that's cool.
"What's better than a explosion? A DEADLIER EXPLOSION"


Redeem the Soul: Taking in count Krieg's suicide behaviour, the +40% time on FFYL which this gives is very useful. Also, this gives more time you enjoy the extra explosive damage from strip the flesh. (This one is optional, you can get it by taking a point from Salt the Wound.)
"It's taking too long to die..."

Salt the Wound: While the shield is down we get some damage, that's cool, yeah, and if you can get more melee damage per hit on you, it's even better.
"This baby steak needs more salt, maybe there's still some on my scar."


Silence the Voices: Massively increases melee damage, but you will surely end up hitting yourself making you go below 50% health, half second before a bullet impacts on your eye. (Also, self- damage is boosted by Fuel the Blood's grenade boost, don't ask why.)
"If I bloodsploded everytime I meleed myself to death..."


Release the Beast: Because you always wanted to have an excessively big arm that you use for chasing those little people that made you go mad. Your buzz axe will get bigger too, though.
"You shouldn't have hit me."


Unleash the hell...


Blood-Filled Guns: This one opens your path to the bloodlust stacks, and makes your magazines bigger, what else would you want?.
"With these guts I'll make a bag to increase my magazine."


Blood Twitch (2/5): Increases weapon swap speed, which is very helpful to slag enemies and change to some boomy boomy weapon.
"THIS ONE, NO, THIS ONE, NO THAT, WAIT THIS BETTER."


Taste of Blood: This one gives you a considerable defense and a very huge ammount of bloodlust stacks with a kill, both while in rampage.
"I wish I felt all the damage, like those guys."


Blood Bath: When you kill an enemy with an explosion (A rare thing on this build), your weapon's damage increases per bloodlust stack, and the enemies you kill will surely drop grenade ammo!
"And that's how the grenades are made."


Buzz Axe Bombardier: Not enough explosions? Attach dynamite to your buzz axe and make people both have a saw on their heads and exploding eyes.
"I hope one of those don't fall at my feet."


Fuel the Blood: This one is like Christmas. When you melee-kill an enemy, the grenade damage is increased based on your bloodlust stacks. This increases bloodsplosions, Buzz Axe Bombardier, Torge stuff, and a lot of more fun things' damage.
"All the Booms go BOOMS"

Nervous Blood (3/5): Who doesn't like faster reload amirite?
"STOP STOPPING KILLING."


Bloodsplosion: The angular stone of this build. With this you'll make all those people around you explode and make others explode too. It's like fireworks, but with more blood and guts.
"I'M GONNA KILL YOU... oh wait, you exploded, I'll kill that guy over ther... Well, he exploded too"



Fuel the Fire: Do you like fire? Do you like pain? Do you like set others on fire? This has everything of that. Increases elemental proc chance by A LOT after a kill.
"Nothing like a gasoline shower before a good cigarette."


Numbed Nerves: Adds a lot of damage resistance while on fire, and trust me, you'll be on fire a lot of times.
"This is fine"[imgur.com]


Pain is Power: This skill adds more damage with pretty much everything (Except sniper rifles), and even more while on fire, at the cost of critical damage. But bloodsplosions can't score critical hits, so it's ok.
"My axe is deadlier when it's on fire!"

Delusional Damage: Allows you to set yourself on fire with any elemental proc, and not just fire.
"All ways lead to BURN."


Fire Fiend: Increases reload speed and accuracy while on fire, and has a 50% (at 5/5) of setting an enemy on fire with a melee hit, which allows you to set yourself on fire while on rampage.
"♫ I'm swiiingin' in the flame, just swiiingin' in the flame. ♫"

NOTE 1: The difference between bossing and mobbing is simple, for bossing you want as much damage from bloodsplosion chains as possible, leaving apart the survivality, so roid shields are our way to go. I'll separate the equipment on those two groups to remark the best ocassion to use it.

NOTE 2: I just put here the things I use most. There are plenty of useful equipment in the savefile I attach in the video if you want to check those out.

Weapons

Pew pew pew! I mean... BOOM BOOM BOOM


1. Slag Source
Slag is the most important gimmick on UVHM, so you'll need a trusty slag weapon. My top 3 is, in this order:

1.1 Slag Pimpernel Banbury, Maliwan grip and Dahl stock

Simply my favourite weapon. A well placed shoot is an almost 100% guaranteed slagged enemy.
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1.2 Slagga Fire Rate + Bullet speed, Maliwan grip, Dahl stock

Another excellent slag weapon. Fast fire rate deep magazine, high slag chance, and 3 pellets per shot.
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1.3 Grog Nozzle Maliwan grip, Evisceration (With Roid shield)/Expeditious (With Rough Rider)

A very high slag chance pistol that also heals you. Krieg has a gimmick that makes him do less damage when he melees with a bladed weapon while wearing a non-Roid shield than hitting with his axe (default melee), so you might want to use each on its own situation.

Evisceration:
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Expeditious:
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2.Main DPS source while non rampaging
Double Penetrating Unkempt Harold (Torgue Grip, Double prefix)
This is one of the best things in the game, and it explodes, perfect for Krieg.
Also, this is too mainstream to not use it.
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3. Auxiliar weapon
3.1 Kerblaster Torgue Grip, Wild, Dahl stock (MOBBING)
This is a great explosive assault rifle, and drops grenades upon impact, which makes it even more deadlier. Also, the secondary grenades get grenade boosts, unlike all other torgue-barreled ARs.
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3.2 Rapier Slag, Vladof grip, rabid, Dahl stock (BOSSING)
Gives you a massive increase of melee damage, creating more overkill damage to boost massively Bloodsplosion chains.
"THIS DOESN'T EXPLODE"
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4.Second wind / Big explosions stuff:

4.1 Baby Maker Bandit Grip, Dahl Stock, Refill, Non-Elemental
The reloads are better if you throw them at the feet of the people you want to blow up, since the child will most likely hit him at the same time.
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[b4.2 Creamer[/b] Torgue grip and exhaust, damage prefix
A massive damage rocket launcher, whose projectiles split in two upon a distance, exploding in the process. Every "child projectile" deals a 80% damage of the inicial explosion, and it also heals since it's a Moxxi weapon.
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Equipment

What sound do all of these do? Plonk? Hmm whatever

1. Shield
1.1 Rough Rider All Maliwan (MOBBING)
One of the best (if not the best) shields for Krieg. Its 0 capacity and its resistance sinergize a lot with most of his key skills and increases furthermore his already high survivality.
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1.2 Hide of Terramorphous All Maliwan, Shock resistance (BOSSING)
The most melee you do to an enemy, the biggest the bloodsplosions are. the bigger the bloodsplosions, the highest the chances of fast killing big boi. Not recommended for mobbing since you lose most of the survivality, and decrease it since you smack yourself with a huge roid boost.
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2. Classmod
Legendary Sickle Classmod
This one increases melee, and some of the most important skills in the build, like silence the voices and fuel the blood.
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Side note: For some bosses you might want to use a blue Diesel Sickle (+6 Fuel the Blood, +5 Silence the Voices) since it has more bloodsplosion potential.

3. Grenade Mod

3.1 O-Negative Slag, Longbow, High Fuse time (MOBBING)
The point of this grenade is to throw a bunch before activating the skill, they'll take a time to detonate, so you will have some extra healing and slagging while on rampage. Also you don't need a stacking grenade since meleeing gives you about 40 stacks per kill, plus you're setting people on fire and gaining extra DoT stacks thanks to Fire Fiend.
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3.2 Crossfire or Bouncing Bonny Slag, longbow, very low level, 0 fuse time (BOSSING)
This grenade allows to cover a huge zone with a lot of enemies in slag, ready to be bloodsploded, or in the other hand, gives more chances to slag a big enemy like some raid bosses.
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3.3 Storm Front Longbow, 0 Fuse time
One of the best grenades for survivality while paired with a moxxi weapon. For bosses you might want a low level one so you don't kill minions while getting stacks.
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4. Relic

4.1 Blood of the Ancients Stats at convenience (MOBBING)
This relic increases Krieg's health, which gives him even more survivality, also the extra ammunition is nice since you might get low from spamming baby makers all over the place.
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4.2Explosive damage Relic
Increases explosive damage... that's good... yup.
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Video demonstration (Savefile in the description)

All the skill pictures were taken from the wiki, so thanks to the one who uploaded them.
The equipment screenshots were made by me.
If I have any orthographic / grammatical error, tell me and I'll fix it.
Thanks everyone for reading this.