This is it, you're encounter with Wheatley, your new arch-nemesis. We'll break each stage to the fight down into a screenshot and then a video of the whole fight in action should you need the extra help.
You now need to step through the portal (so you're now on the upper ledge behind him) and go across to GLaDOS and pick up the corrupted core. Use the blue Repulsion Gel to the left of Wheatley to bounce up and place the corrupted core directly on him.
Get a portal on the wall back up behind Wheatley (same one as before) and then walk to the end of the - now broken - walkway. Drop down and bounce up to catch the second corrupted core. The socket to place this core is on the right side of Wheatley, so use the blue gel in the middle of the room to reach him.
Don't move the portals at all for this round, simply stand behind the portal on the ground and move back slightly as the mines are thrown your way. Wheatley will expose his back again, allowing you to damage him with ease.
Once again use the central puddle of blue gel to bounce up to Wheatley and attach the final corrupted core to him. Once the rain ensues, wait for most of it to clear up and lay a portal on the patch of white gel still present. Now make your way to the stalemate button for a nasty surprise.