The Rockstar Games Social Club is your best friend for this one trophy. As mentioned in the Tips & Strategies, there is an interactive map on the Social Club website that shows the location of all of the spaceship parts (and whether you have collected them or not).

This can be done after meeting a guy by the name of Omega, who will appear as a stranger-mission for Franklin. It is possible to meet him shortly after the mission "Fame or Shame". It doesn't matter which character collects the parts, but Franklin is the one who has to deliver them once you have obtained them all.

Four parts are only accessible with a chopper, so keep a lookout for one if you don't own one.

Be sure to save your game every now and then with your mobile phone after collecting some parts in the case you die!
 

All Spaceship Parts Video Guide