Well it seems that Barbarians will be a repeating event so here we are!
Arctic Barbarians Invasion can be found here in the same menu as your Eggs, Daily login, ect while the event is active.
By navigating to the Monarch Scores page you can see that you only have a certain number of "chances" a day. I put chances in quotes because it's a little misleading. What it really means is that you have 10 SUCCESSFUL hits on a Barbarian Castle per day. So if you hit one and lose, it does not take one of your "chances."
Picking a Barbarian:
First off, there are 6 levels of Barbarians. Most people over K30 are going to ignore levels 1-3 and mainly be looking at 4s as thats where the real points start.
While you may be tempted to just rally the biggest ones with your friends and occupy those. You might be costing yourself points. Save your chances for ones that you can max out the maximum occupying power for. You can see the minimum and maximum march power for points in each City by visiting its Info menu.
The reason you want to use your chances only on one's you can max is because the max points from a level 4 is more than the minimum points from a level 5. For example, the 158mil power level 4s give 3824 points per second when your march in it is max or higher. Whereas the same power march will get you half if that in the lowest power requirement level 5.
Bigger alliances that have people who can march 150mil+ power at a time might look at rallying the bigger level 5s since they can all fill the requirements for max points.
Killing a Barbarian:
Time to test out your Arch march. Have some fun, as the damages taken from Barbarians is very little compared to if you took the same test in SvS or battlefield! With a really strong Archer buff (1100%+) you can potentially solo the weakest level 5 which is the 334mil power as it has lower buffs than the 314mil power one.
If you can't do that, then search for level 4s of 105mil+ power as those will give you the most bang for your buck. I'd say you need around 800% archer attack buff for the 158s, but the 105mil could easily be done with 600%. Make sure you are using a properly layered Arch March that is heavy on the t12s as you would in any PvP situation.
How I've found to get a ton of points:
Your chances are only used if you actually participated in the battle for the city. So if someone else hits a Barbarian and opens it, you can Occpy it without using one your chances. If 3 people in your alliance open 10 105mil+ Barbarians, that's potentially 30 chunks of passive points for you to gain while you do dishes or take a shower or make a Guide on Arctic Barbarians 😉.
First place has some pretty heavy rewards and the top 10 in general isn't to shabby. Top 5 is what gets that beautiful Jade Castle that everyone wants.
But along the way you will get Barbarian Chests as rewards for point milestones. In the end if you make it all the way through, it comes out to a nice chunk of gems for you to spend just for doing something super passive.