Assassin's are f*cking stupid. Holy cow, top players in my games have stacked all six of them and literally not lost a single round. This gamemode is the League equivalent of Hearthstone, anyone can be good if they get lucky. It's stupid.
I love the hex system as opposed to DAC's and Underlord's grid system, but I feel like this is the largest reason why assassins are so prevalent. There's too many openings for an assassin to hit a priority target since every unit can be attacked from 6 total sides.
There are two ways to counter assassins in tft.
First one is blitzcrank. He pulls enemies to wherever he is automatically. So, assassins automatically dive the back line, put him up top and he will drag the enemy up to him and force them to fight.
Second way is going glacial, often with Volibear. They jump into your team and get frozen. Most of the glacial champs are tanky (Sejuani, Volibear, Braum).
Or you can just go Wild/Brawler with Warwick at the start. WW can survive a lot of it by using his ability, particularly if you get early items.
The strats assassins excel at defeating are protect the ADC comps or one champ with 3 items on it.
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Assassins have increased crit rates, build 
and go for things like glacial or wild or noble or shapeshifters.
when you see youre going to get screwed vs a guy stacking assassins, invest in at least 2 frozen hearts and position your carry in the center with tanks and peelers around him, so that the assassins dive the targets you choose, and are extremely gimped. i suggest a frozen heart on the carry for this purpose
My solution is a bit simpler than picking a whole comp for it. Give a carry a guardian angel and nothing else (build up the rest of your team). Put the carry in the back row and your other champs in the front. You can put some in the second row, but put them a bit to the side, leaving some space in between your carry and the rest. The assassins will jump the carry and kill it while your team attacks them. When GA goes off, the assassins will switch targets and your carry can... carry on.. with its business. If you're team is built decently enough, they should be able to out damage the other team from then on.
My formation in this case is usually positioned to the right corners: 3 tanks/bruisers in the top row side by side, 2 fighters in the middle row side by side (the fighter on the right located in the space south west of the left most tank in the first row), and my carry in the bottom right corner.
