#1 - Grapple Gun
In the main storyline after winning in the arena for the first time.

#2, #3, #4 - Power Lantern
In the main storyline after defeating the crypt clank

Also gives Shock Absorber and Earthquake Resonator

#5 - Grapple Pull
Found in the plunder room. Use the power lantern to open the door in the second floor, on the right, far side of the room.

#6 - Wrencherang
Found in the fun room, but entered from the Arena Entrance. In the Arena Entrance, find a grapple anchor to your left in the ceiling. Choose the leftmost exit. When you come back to the fun room you can open a bridge. In this location there is a grapple anchor in the ceiling.
Requires: Dingbot propeller, Grapple Pull

#7 - Rage Amplifier
In the main storyline after unlocking spark power (Death Ray) in the Red Playroom.

#8 - Boom Clank
In the main storyline after entering The Great Movement Chamber, beneath the Red Playroom