The Mini-game is a rewarding gameplay mechanic that can help reduce the stress of grinding and keep the game from getting too repetitive.
Obviously, you don't have to play the mini-game, but if you do you will be rewarded with a loot drop ontop of your character at the time you complete the mini-game. If you are reading this and skipped the tutorial (understandably) then you've probably already finished a mini-game or two without knowing it already!
Where is this "mini-game" and how do I play?Edit
In the bottom right corner of your HUD by your Power pool and Right handed weapon slot are three Icons not connected to the hotbar. Each of those icons represents a task you must complete in order to complete the mini-game.
To learn what each ot the three tasks is, free up your mouse (for example, by pressing enter to trigger chatting), and move the cursor over to the little icons on the lower right. The tooltip that appears will tell you what you need to do. It may be, for example, "Spectral attack," "Eliminate beast monster," or "Acquire sword." The number that appears near the icon tells you how many times you have to do this action to win.
"Acquire" types are self-explanatory. Get a gun, get a weapon mod, get a sword. You can "acquire" it by picking it up as a drop, be it from a monster, a chest, or even a previous minigame reward.
"Eliminate" types are almost self-explanatory as well - when you highlight a monster, its type will be shown near its health bar at the top of the screen. Note that you may be told to "Eliminate spectrals," for example, in a level where there just aren't any spectrals spawning, it's all beasts or necros. That happens sometimes. This can be annoying, but of course you can solve it by going to a different zone.
"Attack" types are a little more complex. To accomplish these objectives, you must do damage of a specific type - poison, fire, etc. Most weapons have one specific damage type. If the damage type of your favorite weapon is not the type that completes your minigame, there are a couple ways around it. You can have an alternate weapon in your second or third slot (F1, F2, and F3 switch weapon slots), with a different elemental type. Alternately, you can slot a weapon mod into any of your weapons that adds a % elemental damage, and the weapon will begin to do all types at once - its base type, plus a little bit of any damage types you've added on this way.
It's important to know that while the "Attack" type kind of implies that you can just do damage of some type - you must actually kill the monster to get minigame credit.
There are a couple more things to know. If you win the minigame, the items it drops can help you win the next minigame. If the minigame triggers and it drops two guns, then the next minigame rolls up and one of your new objectives is to acquire 3 guns, you're going to be most of the way to that objective already. Don't worry about waiting until the new minigame completely rolls up (stops blinking) before you pick up the items; it's already counting them, even though you won't be able to see it for a few seconds.
Finally, a little thing that confuses first-timers is what happens when you need to do the objective exactly one more time. Say the counter starts at 8, and you kill 6 beasts. The counter goes down to 2. When you kill another, the counter disappears, but you haven't accomplished the objective yet. You have one more to kill. The way you recognize this is that the icon for the objective is still shown as yellow line art. When one or more of your objectives are fully accomplished, they are filled in completely, rather than being line drawings. After you see this once, it won't confuse you again.