The Back Alley Brawl challenge is as follows:

Wave-based survival.

Fight your way through increasingly difficult waves of enemies. Each enemy you kill gives you points. Killing enemies with flair gives you more points.

A golden merchant sometimes appears for a duration of 30 seconds. Hit him to earn ammo and elixirs. Kill him to earn gear upgrades. Runes appear randomly in the environment between some rounds. Collect them to earn a new power.

There are rival factions, and they will fight one another. You can use this situation to your advantage, but only your own kills will increase your score.

In the first few rounds of this mode, you can choose to either engage the enemies on your own or let them do the work for you. Engaging the enemies head on will earn you more points that simply letting them kill each other off, but you'll also run the risk of losing health and mana.

We'd recommend saving the conflict for until you've properly upgraded yourself. You'll begin atop a stairway. For the first round, let the enemies below kill each other off until there's only one remaining. Rush down but don't yet kill him. Instead, set your two razor traps in locations where you think they'll be most useful. Place them in bottlenecks, or on the stairway leading to where you started. Now, kill the last enemy, silently or from above preferably to earn more points.

Rush back to the top of the stairway and play the same game for the second round. Once the soldiers remain, rush down and kill them. Stay on the bottom floor for a second; the first Rune should appear after the second round. Grab it and then rush back up the stairs.

The third round's conclusion will see the first appearance of the Golden Merchant (in many cases, at least; this is somewhat randomized, after all.) Beat him up until the timer counts down to 2, then turn tail and head back up the stairs. Use this strategy to force the enemies into killing each other or stepping into your traps until you've collected enough Runes, elixirs and item upgrades to be a real force on the battlefield. Now you can head down and give the remaining waves the fight of their life before you eventually and inevitably die.