Here are some tips and tricks that i personally noticed. I might miss somethings that bigger better player knows. But this is a start for people getting into playing monk on TI.

As an outside monk you got 2 main objectives:

Nr.1 and most important is to makes sure the minions dont go down.

Nr.2 on the flipside you also want to try and be inside as much of the fight as you can; the more dps you get inside the old one fight the better.

Tips:

1. When you fight inside at the old one, you can look at the map to know what wasp fight is coming up.

2. In the old one fight, you can jump backwards outside the platform and teleport out that way. Remember you will loose over 50% hp and loose all your mana.

3. 2-4 player scaling you might consider going for the Wasp Queen kill. 5-6 player scaling the wasps has so much hp killing her might not be fesable.

4. First Wasp Queen can spawn from any spawn point on the map, however the second Wasp Queen always spawn from the south west spawn point.

5. Wasp Queen has lightning resistance. So if you are going for a kill using a griffin pet, be sure to fight her inside the strength aura. Cdragons are much preferred on outside monks. 

6. Loosing the app towers wave 18 is not a big deal. Your focus should always be on minion health.

7. In normal runs you only focus on the first wasp spawned. Only if the lobby runs slow, you might have to devide some focus to 2 or more Wasp Queens.

8. Here's a cool tip; time slows down in TI, meaning the mobs slow down if the defence and your mates die, it works kinda like when a jester rolls slowmotion. If you are in a fast lobby 5-6 people scaling, and the guys inside starts to drop like flies (bad rng or lack of skill), maybe the inside monk dies and you have to go inside and boost your mates. You can absolutly do so! The map rewards fast game play, -the faster you are, the slower the mobs will be! The times you wanna aim for is 4-5 minute runs. 7-8 minut runs the slowdown is barely present, -if even. At that point, you may want to kill the Wasps and barb boss before going in to finish off the old one.

9. Leaving some orcs unupgraded can help the outside monk, as it can be easier to simply upgrade orcs then repair them manually. 

Hint 1: These are the easiest Wasp Queen spawns. With these spawns you can prepare your mindset to be inside alot. South west spawn takes the cake, - with this spawn you can stay in a bit longer than normal. You can do the second trip and help with the hands & chest, sometimes even the head! Check on the map how fast she moves along to judge when to jump out. East and south east spawns you can stay in and help with the hands if the jesters roll swords or rangers/barb are super quick. If not you go out after killing the feet, and keep up boost.

Hint 2: you can lead the outside wasp this way. After a bit she will aggro at the minions at the doorway to the tavern. 

Hint 3: This is a cool one, and helps a ton to go inside and join your mates. When you defend inside the tavern (either side), and the Wasp Queen aggros on you, then you are able to lead her to the orc next to the portal and leave her there. Once you jump behind the orc, you can see when she aggros on the orc instead of you! This is a safe position, as the mini wasp she spawns, will go for either the other minions or the app towers and not the core! By the time they kill all the minions and app towers, you have already finished the old one fight. This may also a desired strategy depending on how many players you are, since the player count contributes to the number of Wasp Queens spawning. 6 player scaling you can have multiple Wasp Queens hammering at the minions at the same time. I do not recommend you lead her up the stairs, as she go back and aggros on the ogre at the doorway when you back inside.

Hint 4: These spawns are the worst ones for an outside monk. You must go out after killing the feet, sometimes right after head if you had unlucky rng on the old one (if you do go out straight after headkill prepare yourself to go in again sooner, as the inside monk can struggle keeping up his boost). In this scenario your boost will still be up. Be mindfull of when you force CD, so you can get back in and help boost your mates in time. 5-6 player scaling you might have to stay outside the rest of the run. Loosing outside minions is detrimental to your run.

Hint 5: Depending on the spawn point, you generally want to stand on the ledge or the bridge to kill the Wasp Queen, bcos harbingers can kill you if you get stunned. If you cant kill her, or if she moves closer to the minions, you can try to lead her of the the tavern doorway (hint 2).

Also: You could be playing Poly instead :)