I'm wondering if anyone else has been having the same issues that I tend to. My runs are always super easy until I run into a champion with the illusion or conjurer affix. 95% of my runs have been lost to one of these enemies.

Is there a good strategy for fighting them? They tend to do about 30-40% health worth of damage per turn, so I never have a chance to portal away. None of my health items heal me fast enough to keep up with the damage output, and I frequently can't even get to the main champion because the summoned creatures are in the way.

Any help would be appreciated, I'm getting really tired of this game because of those two enemy types.

* If you can't reach the main enemy, try using movement skills or ranged attacks. Wild Horse (from Sword Dancer) is a really good movement skill for this purpose, as it moves you a decent distance and lets you attack at the same time; if you can get some Jump Boots, they can boost the range further. Also, some of the weapon mastery skills are movement skills, including the claw and fist ultimates. Don't forget that Brigand has one that does shadow bleed, and Armor Training, when used with heavy armor, can add an additional attack to movement skills.
* Illusions are harmless; all they do is move around. You can use area of effect attacks to deal with them, or you could just figure out which enemy is actually attacking you and focus on that one.
* Sometimes, the item you need to use to save yourself isn't a healing item, but something like a Teleport Scroll, which instantly warps you to any square in range. Use it to retreat to heal, or use it to get close to the main champion (particularly if you don't have a usable movement skill).

Thanks, that's helpful info. I have tried most of those strategies, and they work some of the time. It's no so much that I die every time I take on one of these monsters, but that every time I die, it's because of one.
I also have definitely seen that illusions do damage. I have tested this multiple times, and even when I turn off my pet attacking and have killed the main mob and any others in the area, hitting spacebar to just pass shows that they are still damaging me. I was actually really surprised when I first looked up the illusion affix and it said that they don't deal damage, because they definitely do.

EDIT: So I have had no luck in further replicating the "illusions deal damage" that I had seen previously. I think I either had multiple illusionist champions at once, or I had frog champions summoning more frogs and got confused.

At any rate, I am still having a deuce of a time with summoners, as the frogs kill me so fast and I can't keep up with their damage output. Running away doesn't help when they are guarding the stairs for a floor I need to access. I guess I just need to grind more in my runs.