Mechanics

Movement speed

Grapple swings is the fastest form of movement, but when walking on the ground, it depends on how many speed booster items you have. With no or one speed booster upgrade, constantly jumping is faster than walking. With two speed booster upgrades, walking becomes faster than jumping.

Tricks

Shotgun poke

The shotgun is a long weapon. One tile long! This allows you to hit switches from the wrong side of a wall by simply standing as close to the wall you can, and the thing you need to hit not being more than one block into the other side.

Bazooka poke

Similar to the above, the WASP Bazooka normally can't be fired when you stand next to a wall. However, given how it works, you can start holding the fire button so the beam turns green while away from the wall, and then poke the bazooka into the wall and fire. This allows for hitting switches even further on the other side of solid objects, but can sometimes be unreliable. Even without the poke, the bazooka is capable of hitting switches one tile into a wall by simply shooting the wall.

Grapple through solid barriers

Found by Greenalink
It's possible to fire your bionic arm through solid objects and collect items on the other side, something that allows for collecing both the WASP Bazooka and first speed booster upgrade in the first stage. To do it, do a slow walk towards the object while holding somewhat down so your bionic arm will get launched horizontally when you fire it. When it's been launched, before making contact with the object, turn around. This will cause the hook to lose collision detection, allowing it to go through the wall. To collect the item, you need to give it back collision detection by turning back towards the wall, and then ducking to make it actually hit the object. These movements are very, very hard to do in real time, so make use of biovision buffering: By holding down RT and activating biovision, every action on the screen stops, and by holding a direction when you let go, that direction will be input when you let go.

Grapple through the floor

Found by Greenalink
You can grapple yourself into the floor by making use of one-tile objects such as barrels standing on the ground. To do it, move up right next to it, then crouch and fire your bionic arm to attach to the object. Then hold up and hit the grapple button twice in rapid succession. If done correctly, you'll now be hanging underneath the objects and can reel out the arm into the floor. This allows for skipping significant parts of the levels Robot Factory and General Headquarters.