The Gunslinger Award is earned for killing all enemies in all waves after the initial wave without towers damaging any enemies. Non-damaging Towers, Traps, and Auras are allowed to slow down and impede the movements of the enemies. They are the Magic Blockade, Gas Trap, Darkness Trap, Ensnare Aura, Healing Aura, and Strength Drain Aura. All types of familiars are also permitted.
The Squire's Spike Blockade can be used for a more durable alternative to the Magic Blockade, but it must be placed backwards and enemies cannot be allowed to circumnavigate it. Auras are an effective complement to all blockades, and helps to keep enemies from moving around them.
I've found that Series EV 's physical beam is the best wall for Brute Force. Her walls can be any length, thus being able to fit in much more places than a backwards barricade. Her walls also do not damage enemies so even if an enemy (usually an Elf Warrior) slips past your defences, there's still no worries of damaging them.
Alternatively a second player can be used to set up a total defense as normal. This allows the "gunslinger" to focus solely on hero damage and earn the award easily. The Barbarian (PC only) is an excellent hero class to use since he cannot build defenses anyway.
Note: It may be a bug, but sometimes upgrading other players' defenses counts stops a weapon-only player from getting the Gunslinger award.