Okay, so as soon as you jump in, you have to pick a team of seven cards.
Most of it is pretty cut-and-dry, but you may notice two sets of levels.
The first level is the standard level, including EX levels. No big surprise there.
The second level (shown as Lv. MAX in the picture) is a separate level that can only be increased by drawing the card again. EX wilds will not affect this. Any future reference to this level in my explanation will just be called "red levels".
After you make a team, you pick a card from your friend list.
I'm not 100% sure what determines what your "assist card" will be. Probably just whichever one is first on your team or something.
So you now have a team of eight cards, friend list assist included. At this point, it becomes similar to your usual Elite Guard event until you get into the fight.
Most of it looks the same, except...
The listed SED is the minimum if you use a 1-focus attack. More powerful attacks will do more damage, but will burn up more focus.
So you've got your team, you've got your opponent, you go to lay waste and...
Yeah, you're not gonna do much unless you attack a lot, attack harder, or both. Slayers are more powerful, but they don't increase your entire team or total SED like they normally do in EG events.
To help you out a bit, you'll occasionally get these cut-ins of some of your teammates.
I'm not 100% sure, but I want to say maybe these are critical hits or something. Again, I'm not positive because they occur on a per-character basis and the attack power is pretty random already. It does seem to be based on the character's red levels, because only characters with red levels will have these cut-ins and they seem to happen more often with higher red-level characters.
While I'm still a little shaky on what red levels do, I think they're pretty important because the game seems to put a lot of emphasis on getting copies of the same card.