Saving ClaudeWhen you enter the level, walk straight forward and climb out of the small area which you are placed in. After listening to Juliette's attempt to get her husband to talk back, grab a Plasma Blaster/Beamer if you haven't already got your paws on one, and start attacking Claude with it. You'll only cause him damage when you attack him with Energy beams, so don't switch from this weapon! Claude has his own energy beamer, so make use of your exaggerated leaps and bounds and avoid touching them at all costs.
After a while he will fly into the air. Run around and dodge the beams he shoots at you (It sometimes helps if you shoot back at him). When he lands, continue shooting him. When he flies up into the air and the ground starts shaking, quickly run around to the main base. The ground will collapse soon, and there's nothing to support you should you fall! A new door will open up above you once the ground has gone. Now climb the wall with the Cat Scratches on it and you will be in the next area. You'll then need to repeat this process twice more.
Claude will stay in the air longer as each floor collapses, and he'll require more hits before he moves forward. Use the Pet Yums and extra ammo if you need to. If you do miss any floor besides the first, you might be able to still land on the space station and crawl back up to the floor you were on.
Eventually, Claude will collapse, and you can continue on your adventure.