Hellgate London Guide

The mini-game is a game within a game in Hellgate: London that rewards you with extra items upon completion. It is in effect at all time during normal play that gives you something to think about while killing monsters and picking loot.

Monsters to kill
Kill Beast-type enemies
Kill Demon-type enemies
Kill Spectral-type enemies
Kill Necro-type enemies

Damage to deal or receive
Deal critical damage
Deal or receive fire damage
Deal or receive electrical damage
Deal or receive spectral damage
Deal or receive toxic damage
Deal or receive physical damage

Items to loot
Loot an enhanced items. Enhanced items are any item of green or better rarity.
Loot a mod
Loot a ranged weapon
Loot a melee weapon. This can be difficult to achieve for ranged classes, since swords are fairly rare drops for them
Loot a piece of armor

Other
Quest Completion. You need to actually complete a quest to achieve this goal