1) Play armor. Playing a chest piece will really help. If you aren't sure what your opponent is doing you can usually afford to play a Brace Yourself without disrupting your opening too much. Your opponent will almost certainly try to remove your armor, and it's important to keep reapplying your armor if they do. If you can maintain your armor against your opponent, Veteran's Belt makes that armor even more effective.
2) Play a defense. Block, Reverse Attack, Cobra Reflexes, Reflex Boots, and Force Orb are all helpful against this style of play, and make big attack spells much less efficient. Block and Reverse Attack are more stopgap measures than the others, but can still do wonders to make a hyper aggressive mage run out of steam.
3) Block line of sight with walls or otherwise prevent your opponent from targeting you with those attack spells. Cloak of Shadows and Fog Bank are also options as long as you can limit your opponent's mobility.
4) Play a creature with Intercept. A Guardian Angel, Dwarven Panzergarde, or Gargoyle Sentry can do a lot to take pressure off your mage from attack spell spam.
5) Heal. This is less important than making sure your opponent can't do massive burst damage to you, but if you have 4 armor and a defense, healing is much more efficient than attacks against you. Just make sure you don't run a Heal into a Poisoned Blood, since that sets you back pretty far. You can use direct healing spells, though I mostly do that with the Priestess. Other options include Vampirism and Regrowth Belt.
Daze/Stun chances are helpful, though not as strong against attack spells as against mages reliant on non-spell attacks.
