Are there any specific ways to best jungle as him? what routes should I take? what masteries and runes should be taken? What items should i build on him? When should I start ganking lanes? how do I know if my jungle is being invaded and how should I react if they do? when should I invade the enemies jungle? When should I engage a fight? Who counters him? How can I improve my bola accuracy? What level should I drag?
the only thing i know about rengar is how to 1.shot somebody. Use empowered Q before you leap on your target, it should go off in the air, near landing, make sure you use E and W and hydra if you have one. As for ways to improve bola accuracy, make a bot game and stand in a brush and practice throwing your bola when in air. Dont engage fights, wait for enemy CC to be blown then go for isolated carries. Runes should be AD quints/marks arm yellows/mr&cdr blues(up to 5% cdr). For masteries just look up Nightblue3 on lol king and search for his rengar page.
The route I always take on my junglers is this-
Red side: Gromp-(early scuttlecrab if you have bad sustain)-Blue-(wolves if you have good clear)-krugs-Red-recall
On 
I usually have to back before red. You might get executed if you aren't too experienced with him.
Runes/Masteries: I can't say what specific ones but 21/9/0 and for runes I take AD reds, armor yellows, CDR blues and quints of AD/Armor. However, those are just the ones I take and are very interchangeable.
Items- I usually go 
if I can. I really like that build. If I get fed I build an 
and if I'm laning I build 
with my hydra. 
I take for defensive items.
When to gank- level 6. Your ult helps you get into the lane undetected and leap onto the enemy. I usually follow it up with a full-ferocity bola so my laner and I pounce on him.
When is your jungle being invaded/how do you know- You know usually if your buffs are gone but their minions are there. I can't give you advice on what to do if you get invaded, though.
When should you invade- I usually don't on . All I know is that, if you are playing a non-ranked game like with friends or something, it's possible to do a level 2 invade and get first blood by leaping out of the bush when the enemy is low health fighting a buff.
When should you engage a fight- When only one or two enemies are alone and they aren't that tanky. If there are two of them, make sure you have some allies nearby as well.
Who counters him- CC, kite, and tanks before he gets his armor pen. He sucks at teamfights as well. Also note he uses basic attacks as his main damage output. Some examples of counters are 
Improve bola accuracy- Make sure no minions are in the way. That's all I know.
Level to take drag- 8 is a good level to drag on . May not be a good idea to solo it, however.
Hope I could help.
As a Rengar main I assure you that he's not a complicated jungler to play. Once you can learn him then you will be the terrifying stabby cat.
Rengar should pretty much always start Krugs, the gromp benefit is out-weighed by the Krug's stun which is 10x more useful on someone like Rengar. I usually end up going 
because his early clear is quite awful compared to the more popular tank junglers of today. Blue jungle item is alright and challenging smite isnt really necessary because rengar isnt a dueling champion.(you will lose most duels in the jungle with todays popular picks). Try and always make sure when you're ganking you're around 4 ferocity stacks, it simplifies things immensely.
Skill order should never really change, R > Q > E > W
Build order that I hold as my tried and true build
Your 6th item depends on how exactly you are doing.
Fed as shit?
Split push?
AS for something like tank rengar, just dont do it. Rengar's viability comes from his ability to one shot squishies, take that away and well he's an awful tank with bad initiation, bad teamfighting, bad peel. Your goal is essentially blow everything on the priority target, usually adc's and thats really it.
This combo is the one I use and should probably be mastered by all Rengar players
5 stack ferocity > Ult > Youmuu's > Proc Q > Hydra while leaping > EW(At the same time) > Q again if targets not dead.(Max damage with this combo was 2056 with crit)
Champions you should never pick rengar into
Hope this helps!
