Find the following locations to locate the corresponding orbs. Note: An orb becomes equipped when discovered and you can equip or unequip orbs in your room. Also, you can only equip one resistance and one ability orb each at one time.

White
Clear Lala's house of bugs and take the orb (not the money). This orb gives resistance to light attacks.

Orange
After mission 2, in the great forest, the orb can be found under the cover of trees, in the lower left corner of the second screen. Press TAB to find it. This orb gives heat resistance.

Red
After mission 3, in the first screen of the deeper downs, there is a hidden opening in the upper right corner. Enter it and open the chest to find the orb changes Pyro Blast to Pyro Hail.

Indigo
After mission 4, find the green tent (courtesy of Bill Bob) in the great forest. After buying both "gaggets", talk to Bill Bob again and he will sell you the orb. The orb changes Mind Shield to Big Shield.

Blue
After mission 5, talk to Grotius about being lonely. Then, talk to Nightling by the palace about Grotius. Return to Grotius to receive the orb that gives cold resistance.Green
Between missions 5 and 6, talk to the pirate to the right of the dock at Lake Alto, and follow his instructions to receive the orb that raises speed.Yellow
Go to the island in Lake Alto after saving Darkeye, at coordinates 1806, -846 to find the orb that raises focus.

Black
At the academy, talk to your brother to receive the orb that gives shadow resistance.

Head to the dagger thrower and get gold, then go to HQ. Go to the blue darkling. Now, go back to the dagger thrower. You'll get lots of gold over time.