What would you suggest instead?

Wrong runes -1

Title "Oh Bear, It's Udyr" would earn an upvote by itself.

Even after his nerfs, Zhao is an incredibly strong champion, and he probably has the best level two ganking in the game. The slow and knock up is very strong throughout all stages of the game. He is in my estimation the single biggest threat to Udyr in the jungle. Not to say that others can't be strong against him, but that is consistently the hardest match up I've had.

Udyr excels against champions who are remarkably position dependent. Vi and Yi come to mind as the most common examples of this, but Pantheon in the jungle can get shut down hard by an Udyr.

Udyr's abilties decrease by twelve points from rank one to rank five. The problem isn't so much that his individual costs are high, but rather how often you chain your abilities together mid to late game. Spirit Visage and Crucible are statistically worth about the same amount of gold, which is a selling for Visage. But let's look at what you're actually getting. 20% CDR is...okay, but not a selling point. 200 health is nice, but it doesn't make a huge difference to how you play him, especially since we're building tanky. The MR is wonderful, and unarguably better here than for Crucible. The passive combined with Turtle Stance is really intriguing, but ultimately not INCREDIBLY important. It's nice, but you won't miss it.

I would argue that the health regen is better on Crucible than Visage, because it's constantly working despite your active stance. 40 MR is not as good, but it's close. The mana regen is incredibly useful. The active working on yourself OR a team mate is the winner here. The utility and protection it provides is wonderful. A big part of why I go Crucible over Visage is how you're able to recipe the items for the immediate benefit.

QSS is an interesting option. The active is better at removing threats, it has half the cooldown, and the MR is slightly better. It would also increase the chances of getting a late game Scimitar. If you could use the active on your team mates, then I would get this item every game, even for a price increase. But the fact that it's entirely selfish, as well as less universal in its stats leads me to normally want to spend the extra money.

Have you done any tests to see what other junglers Udyr counters? What about junglers that counter Udyr? I also question taking Mikael's Blessing on him. Providing health, mana, and magic resist is definitely good, but there are more dire items that he should get.

As Udyr levels his skills up, the cost of them goes down quite a bit, especially once they rank 5. Sure, Crucible does help answer his mana problem EARLY game, but you should NEVER get it early. A Spirit Visage is a much more suitable replacement since it gives more of what Udyr needs. Spirit Visage doesn't give as much mana resist as Mikael's Blessing, but that extra health that Spirit Visage allows him to soak up a good amount from an AP's main damage source (assuming that it does between 300-400 damage).

I could see Mikael's Blessing working if the enemy team comp was composed of Ryze, Lux, or Veigar because of the active It gives you, but I would much rather pick up a Quicksilver Sash if that is the case.

Overall, very good guide.