Core / root / foundation: Dark Seal + Liandry

There are two approaches to this, some Udyr players like to buy seal on their first recall, or even second, and there are other Udyr players that believe that delaying your Liandry by 350g is too much, and that you should buy it after.
Liandry and a 10 Stack dark seal will hard carry your damage, especially amped by liandry passive, and the ability to flex into Mejai at any point, you are also backed by Gathering storm as the game goes on if you choose to take that over waterwalking.


Boots:

Say it with me:
"WE DO NOT BUY BOOTS FOR DEFENSIVE STATS, WE BUY THEM FOR THEIR EFFECT".
Ok, now we can proceed.

[Mage] Sorcs: In the mage build, you're ALWAYS taking sorcs, the damage jump is through the roof.
[Conq tank] Steelcaps: If majority of enemy damage is coming from auto attacks, we'll be going steelcaps, this is actually majority of games that this is true.
[Conq tank] Mercs: If enemy has champions that are GOING to land CC on you 100% and the duration is so long you will die during that CC, you must build mercs. (some crazy examples of this are: fiddle, leona,twisted fate) DO NOT BUILD MERCS VS KNOCKUPS,tenacity doesn't work.
[Conq tank] Swifties: If enemy has MULTIPLE sources of slows (Zilean,Ashe,Rylais User or Lissandra) swifties value goes through the roof, unfortunately some games like that it's likely better to go mercs with DMP because of CC duration
[Conq tank] Lucidty / Ionian: If you're so snowballed by Liandry completion, if you know by 10-15 minutes the game is already over, you can win more, win faster with these.



Mage Core:

Liandry: Mandatory AP Udyr item. 6% damage amp

Riftmaker: Extra beefiness, 8% Damage amp + omnivamp + hp -> AP conversion

Bloodletters Curse: 6% damage amp, AP black cleaver, easy to apply and contains hp. Consider moving this to 2nd item purchase if your team is very indexed into AP, and enemies buy MR early (galio mid, zac jungle)

Mejais: Our best item, IF we play to protect our dark seal stacks, this item is so broken. It can be argued that this is a mandatory purchase every game.

Rabadons: If you don't have a 6-10 stack seal by now for some reason. Better than buying multiple defensive items, as your Awakened W will be way more insane, as well as RR threat is going crazy, double synergy with gathering storm if you take that over waterwalking.

Shadowflame: Banger vs squishies, they pop quickly.

Zhonya's: Really good vs insane dive and cc, high priority item vs spells like: Wukong ult, Sett W, Zed R

Banshee's: AP item containing MR, the shield may come handy if you're able to preserve it.

Armor items (conq tank build):

Frozen Heart: We CAN just do the Pentaless Nunu deluxe. Liandry -> Frozen Heart for the armor + CDR, haste is OP, and since Liandry doesn't give you haste, this makes having a Haste item 2nd very nice for spamming spells at our 2 item fight. He builds it every game regardless of the effect being useful on enemies (slowing their AS) the one downside of this item is that it doesn't contain HP. When you build this item, make sure you buy a ruby crystal afterwards, with the negatron from Kaenic.

Dead Mans Plate (DMP): Similar to Pentaless' Approach to Frozen heart being good regardless of the effect on enemies, you're able to just go DMP 2nd on Udyr regardless of the effect of slow resist. You can brain off go DMP 2nd everygame, and the movementspeed, and bonus frontloaded damage will feel good. Synergy with Celerity also feels nice.

Randuins Omen: Any time there are 2+ sources of crit on enemy team, the value of this item skyrockets (think of: GP top, Viego jg, Draven or cait ADC). I think this is the best armor item because it's 75 armor (the highest of all armor items and contains the most HP) It's also 200g cheaper than DMP (2700 vs 2900).


Magic Resistance Items(conq tank build):

Kaenic Rookern: THE premier MR item. 80 MR, you will legit take no damage, and negatron buy is so OP. 850g for 45 MR.

Force of Nature: 125 MR + a ton of MS when fully stacked, ONLY build this when enemy has built in DoT / Burn / Rot champions. Brand, Malzahar, Teemo, Swain, Mel. TThink of any liandry or blackfire torch user. One spell from them, and you're sure to have a fully stacked item that turns their damage to nothing.

Spirit Visage: Bad item: ONLY build this when the following conditions are met: You have an insane HEAL+SHIELD support: Sona/Seraphine/Milio, especially with additional external shielding like a shen R in the same game, this item has insane value because you MUST be grouping and fighting near "Aura" allies (sona and seraphine have radius spells that hit everyone around them). **** stats as a standalone item, and only shines when the conditions are met. DO NOT build this vs Akali,Leblanc,fizz or any real AP one shot threat, they will nuke you.

Tanky Capstone items:

Jaksho: is really nice, especially since you don't have the most amazing tank stats (if you went deadmans or Spirit visage)
Protoplasm harness:If they have no crit, and you already have Jaksho, this item heals you a ton based on how much resistances you have, and keeps you alive nicely late
Randuin:Nice vs many crit enemies