Greatest Kingdom in Middle-earth
Minikit #1 (Free Play)
There are five bird's nests on the statues in the background of the opening room. Use an archer to snipe all five, and you'll receive a minikit.
Minikit #2 (Free Play)
When you enter the room with the two scales, look to the right for a stack of boxes holding a minikit. Smash the nearby cart for some loose bricks, then build these into an action pad. Use a character like Sam to burn the boxes away, freeing the minikit.
Minikit #3 (Story Mode)
In the lower left corner of the anvil room is a throne. Use Thruin's hammer to smash it away, revealing a minikit.
Minikit #4 (Free Play)
In the opposite corner is a pair of locked cages. Use an archer to pop off the targets and open the cage, then switch to an evil character like Sauron to bust open the Morgul chest and uncover another minikit.
Minikit #5 (Free Play)
There are five pots that hang in the same area. Shoot them all down with an archer to receive a minikit (they take a few shots each).
Minikit #6 (Free Play)
When you reach the mines, look to the southeastern edge of the cliff. Use a shovel-wielder to dig up the dirt here. Build the loose pieces you uncover into a turnstile, then use this to hoist a minikit up to you.
A Fire Drake from the North
Minikit #7 (Free Play)
At the end of the walkway is a Mithril grate. Use a character with an explosive attack (Saruman, for example) to blast through and reach the minikit on the other side.
Minikit #8 (Free Play)
When the courtyard gets destroyed, look for this large magic stalactite. Hit it with a magic character to put out the flames below, then you'll be able to grab the minikit.
Minikit #9 (Story Mode)
When you reach the treasure room, head up the gold beam on the left. Smash through the panel here to find a minikit inside the column.
Erebor Was Lost
Minikit #10 (Story Mode)
When running from the drake, keep to the middle of the path. You'll grab a minikit on the way out the door.