Tanking, in typical sense, is not possible in Spiral Knights. There is no armor or shield combo that can absorb massive amounts of damage. Even the strongest defenses in the game only slightly improve your survivability. It is much more important to dodge and shield at the right times than to take a blow.

The only way a shield is going to last more than a few consecutive hits in T3 is if the shield exactly matches the attack. So if you are hit by a Fire Zombie then you better have a shield with Normal/Shadow/Fire, otherwise it is gone in 3-4 hits regardless. There are many different kinds of attacks in the same strata it is going to be hard to pick the right shield if one with the right stats even exists.

The most tank-like shield is the Volcanic Plate Shield, or VPS. It has more health than normal so will last about one hit longer against the average attack. But still, a shield that perfectly matches the attack is going to last 2-3 times longer than a VPS.

Armors are much easier to match up. To resist the most damage you'll need to only match the damage type on both your armor and helm. So, again, a Fire Zombie attack will do the least damage in T3 if you use Normal/Shadow on both the helm and armor. Any fire resistance on the armor only counts if you actually catch on fire, in which case you'll not burn as long or as hard.

The most tank-like armor is the Ancient Plate, but it is only Normal defense so pure Elemental/Piercing/Shadow tears it up. Split damage or pure normal it does very well against. Plus the armor has some nice HP bonuses. But this armor is only available my defeating Vanaduke repeatedly. Besides that might consider the Volcanic Plate Set, but ASI penalty is annoying. You can overcome that though with a 5* Sword Quickstrike Trinket... but why bother when Skolver or Vog has a bonus and provides almost the same amount of defense? The difference is only about 1/2 pip of health per hit.