I am a young grad student, also having the luck to be collaborating a bit with a (rather) big shot. Of course, it would be nice if he gets a good impression of me for the future, as he could probably be an excellent reference when it comes to finding jobs later. But probably, the same discussion applies to any senior researcher you're working with.
Now, the first logical thing would be to work very hard thinking outside the box on problems, using creative, a bit unconformistic approaches in order to try proving that my intelligence and deep understanding of the topic are beyond average.
The other thing is just nicely executing the suggestions by him and the other collaborators, being an efficient, obedient employee outside the spotlights, such that his 'factory runs smoothly'.
On the one hand, the second possibility does not seem to really allow distinguishing myself; on the other hand; the first possibility may come across as a bit annoying by trying too hard to impress;also it is apparently often a good idea to play a bit dumber than you really are ('Never outshine the master') .
To be clear, I'm quite sure I'm in the end still far weaker than him, but I can spend more time thinking on the same problems.
A concrete example: if he suggest something and I've thought of that myself before, should I tell so?