Level: PC Level +0 (or as needed)
Complexity: 5 (requires 12 successes before 3 failures).
Primary Skills: Athletics, History, Nature, Perception, and Thievery.
This all sounds good. I think it's worth noting that in the original Skill Challenge chapter, "primary" skills where any that were listed specifically in the challenge description, even if they didn't provide a success. "Secondary" skills were any skills not listed, which the DMG advised be allowed only once and/or at a Hard DC.
Now, I know the exact conditions of Victory and Defeat will depend greatly upon the game in which this is inserted, but I want to say again how important it is to have interesting Victory and Defeat conditions. For example, if you fail before finding the beast, how is that made interesting? It must be kept in mind. An interesting Victory/Defeat pair is more important than the level, the complexity, the difficulty, or the skills chosen.
Finding the Beast (2 successes)
Nature (Moderate DC): The PC tracks down either the nest or hunting grounds of the beast so they can attempt to capture it.
Perception (Moderate DC): The PC tracks down either the nest or hunting grounds of the beast so they can attempt to capture it.
First of all, I'm not necessarily married to the model of skill challenges in the DMG. I happen to like it, it happens to work for me, but I recognize that there are other ways to handle skill challenges. As long as there's a framework that can help the DM deliver defeat without feeling like a spoilsport, I'm all for it.
That said, I generally don't care for linear skill challenges that require certain skill rolls occur before certain others. I'm not sure what it is. I guess I like the abstract, free-form nature of skill challenges and setting that kind of a barrier for the sake of realism seems wrong to me. Then again, I'll gleefully lock up certain skills in a challenge, requiring other skills to come into play. And come to think of it, The Negotiation locks History away behind Insight.
I still think that if a party wasn't interested in the finding part of the challenge they should be allowed to just narrate past it. They'd get no successes without actually making rolls, of course, and the DM could cheerfully run them around the countryside and into all kinds of trouble before letting them deal with the trapping rolls, but generally a success should be a success.
(You could also split this into two challenges. I find that challenges work better when they're focused on one clear goal. I guess that's part of why I don't like blocking off skills. Make finding the beast its own challenge, so if the players decide to ignore it, they are defeated. This wouldn't mean that they couldn't then face trapping the beast, but the defeat in the first challenge should put them at a disadvantage in the second, say with penalties to their rolls.)
The other thing here is that Nature is being used in a way different from how it's described in the book. That's fine; one great thing about skill challenges is how they can expand what skills can do. The only problem with it is that it might depend on the DM to offer the skill to puzzled players. If they know they need to find something, and look through the skill descriptions, only Perception will really apply.
Nature should definitely apply in this challenge, but I think it should have a different meaning attached to it. I think Nature should tell someone where a creature might tend to be found during certain times of the day, or what kinds of foods it likes, etc. This could be a straight success, or provide a bonus to the next check (or a penalty on a failed Nature check).
Setting & Springing the Trap (final stage)
Athletics (Vs Fortitude): The PC grapples the beast to exhaust it for the capture. A successful check adds one success to the challenge. A failed check causes the PC to grant combat advantage to the beast for one round.
Athletics (Vs Fortitude): The PC wrestles or throws the beast into a better position for the capture. A successful check allows the PC to slide the beast a number of squares equal to the PC's Strength modifier. A failed check causes the PC to grant combat advantage to the beast for one round.
I'm all for skill challenges during combat. Seems here as though the monster is using normal combat rules, but the PCs are expected to use the special rules of the skill challenges. This can work, but there's got to be a reason that would occur to them. You could state that the condition of their contract is that no weapons or spells be used on the creature, for instance.
Then there's the fact that there are already rules for grappling and moving creatures: the Grab and Bullrush rules. Again, without being told how the skills work in this challenge they players may be at a loss. It's fine to explain different rules in a challenge, but some people prefer not to have to do that.
Athletics makes sense for this challenge, but maybe some other application of it, such as helping to rig the trap, getting into an advantageous position, or the like.
History (Moderate DC): The PC uses careful planning of the area to determine optimum placement of traps and use of terrain. This is good for one success before the trap is sprung.
History for this seems like a stretch to me.
Nature (Moderate DC): The PC uses their knowledge of the beast to lure it. A successful check pulls the beast a number of squares equal to the PC's Wisdom modifier. A failed check causes the PC to grant combat advantage to the beast for one round.
Same issues as with Athletics.
Nature (Moderate DC): The PC sets a trap for the beast that hinders either it's mobility, or its ability or will, to fight back. When a trap is set, the PC has to determine what square it will affect. A trap has a DC to notice it equal to the PC's passive Nature check. A successful trap weakens the beast's ability to resist capture (see below). A failed trap causes whoever is nearest to the beast to grant combat advantage to it when the trap fails.
Another non-obvious use of a skill. It's also not clear what kind of action you imagine this to be. I could see a knowledge of Nature being useful in constructing snares and lures, but not on the time scale of combat.
A mobility trap reduces the creature's speed by one square. The beast may be affected by as many mobility traps as it has squares of speed. A successful mobility trap adds a success to the challenge up to a maximum number of successes equal to the beast's speed. If the beast's speed is reduced to zero squares by means of these traps it is afflicted with the Restrained condition until it makes a successful save. On a successful save, the creature returns to having only one square of movement speed. Further traps return the beast to the Restrained condition but grant no further successes.
A combat hindering trap imposes a -2 penalty on the beast's attack rolls. This penalty is cleared upon a successful save by the beast. These traps do not offer any successes toward the completion of the challenge.
Fine mechanics, except for what I've noted above.
Thievery (Moderate DC): The PC sets a trap for the beast that hinders either it's mobility, or its ability or will, to fight back. When a trap is set, the PC has to determine what square it will affect. A trap has a DC to notice it equal to the PC's passive Thievery check. A successful trap weakens the beast's ability to resist capture (see below). A failed trap causes whoever is nearest to the beast to grant combat advantage to it when the trap fails.
This skill use makes more sense, except in how long it might logically take to make said traps. I perfer not to mess with opposed checks in skill challenges, but as yours is closely tied to combat, I suppose it makes sense.
I've been fairly harsh here. I'm not a skill challenge expert. I just know what I like and what I've seen as fun. I hope my feedback helps. I'd like to suggest that you try running this challenge as a Danger Room here in the group to help you find and work out any issues this challenge might have.
Best of luck.
[N]o difference is less easily overcome than the difference of opinion about semi-abstract questions. - L. Tolstoy