Once Elmer's energy bar has appeared in the bottom-left corner of the screen, he will start chasing Bugs around the arena; jumping on him is ineffective so you shall have to jump into one of the four rabbit holes, tunnel towards another one and jump out of it (because when Elmer peers into the hole Bugs first jumped into and says "Yoo-hoo? Wabbit?", you will have to run over to him and kick him). Once you have done so, he will shout "Ouch!" and drop a Golden Carrot (he will also say "Ooooooh..." and drop another Golden Carrot when he hits the arena wall) - and once you've repeated the process twice more to knock him out he shall drop the level's only Clock when he hits the arena wall for the third time. Once you have collected all five Golden Carrots and the Clock, you shall have to jump into the fifth rabbit hole that has appeared in the centre of the arena to exit this level - and once Bugs has jumped back out of this level's hole, Merlin shall appear to him and say Great. Just perfect. You have completed this level. before showing him that (because he now has 37 Golden Carrots and 11 Clocks) he has now opened Follow the Red Pirate Road, but he cannot enter it until he has learned the Super Jump spell (or he times a perfect jump up to the hut containing the wheel that makes the skull rock's jaw drop off the top of the signpost). He will then say Let me save your position.; regardless of your answer "YES" or "NO" you will now have to activate the Time Machine, then move it right twice to select The Pirate Years, press 
(Windows: ) to enter it, and jump into the only open hole out of the skull rock: that of the level Hey...What's Up, Dock?, which is the first level with Acme Boxes (it also has a boss fight against Yosemite Sam, which involves throwing the TNT he hurls to Bugs back at him).
Note: Sometimes, when the fifth rabbit hole appears in the centre of the arena, Bugs shall not be able to jump into it and exit the level; in this case, you shall have to pause the game by pressing (Windows: ), select "EXIT LEVEL", and when prompted "DO YOU REALLY WANT TO EXIT THE LEVEL?", answer "YES" to return to the level selector area (you also have to do this after collecting the remaining items in the three "revisited" levels).