Well, there are a few different ways you can go in defeating the FM. I'll go from what works the best to least.
1. Direct Damage. Damage through things like Ghoul Rot, Mage Bane, Poison Gas Cloud, or Burns even are an incredibly effective way to deal with the FM's Fluffy life total and hefty defense. The actual damage amount may not be very high, but it's a great start at hurting the FM. But, I usually won't throw something like a Ghoul Rot on the FM until like about 24-26 damage, as this guarantees she will either have to deal with it or die. How do you get that first 3/4 of her life chipped away?
2. Unavoidable attacks. Having cards like Perfect Strike, Sniper shot, and Falcon Precision work incredible against the FM. They all get right past her defenses and go straight for the throat. Cheap unavoidable attack spells such as flameblast will often do direct damage in the form of burns, dice damage, as well as getting past the defenses. The downside of that play is that you have to get close to the FM, which can be painful if she has Gravitar equipped.
3. Kiting. Often FM players are hyper aggressive and don't have a long game. If you can kite the opponent, using teleports, force holds, tangle vines, walls, etc. long enough that they can't get much damage into you, your chances of winning greatly increase. If you can kite WHILE doing damage, even better. Out tempoing the hyper aggressive FM is often the best path to victory and the best way to do that is to avoid them and throw unavoidables at them.
What makes the FM so strong is that any one strategy will not work as effectively against her as multiple strategies at once would. So when I see the FM across the table, I will use a combination of these three strategies to get around the FM's soul crushing combo chains. A common pitfall most players fall into is attacking the battle forge. Unless you have a Brogan or something with an insane amount of piercing, it is often ineffective and inefficient to go after this meaty spawnpoint. Often, it is better to tele and keep them out of range from the spawnpoint. This is cheaper, more cost effective, and contributes more to your overall plan.
The FM really isn't terribly difficult to play against, you just mostly have to realize that altering your strategy to something completely different will often lose you the game. You built your book to do one or two things. The FM banks on forcing you to do something else. Stick to your plan.
As well, don't be afraid to dispel a forcefield. Think about it this way: I am spending 12 mana to dispel this card. That is what, 1.2 rounds of channeling? Sure, that's an entire round. But if I instead waste actions dropping counters, that is effectively 3 rounds I have wasted, just to have to waste another each and every turn. Sure you can use the Wall of Thorns/Push combo to remove them, but save that for when the damage is actually done. For one more mana you are getting rid of the card completely! So many times have I seen players try to play around this card. Just deal with it! I promise you will be happier in the long run.
Guarding with 1-2 creatures in the same zone as your mage is another interesting way to deal with the FM and is often under looked and undervalued.
Really man, as I said before, don't let her abilities take you away from your strategy you built your book around. If it is a strong strategy and you amend it to include some unavoidables, kiting, and direct damage, you should be fine!
Cheers, and good luck to you my friend!!
Dude