The extra life from the carrot is actually quite useful. Think about it this way ... without it you will always die earlier on in the game than with the carrot. And especially if you get to the boss with 1-2 lives, that life can really get in handy.
So my recommendation is to first beat the boss.
For this you only wanna enter the PDs where you gain lives in an average game.
The ones I would definitely not recommend to take are PD64 and PD82, since those two are very likely to cost you lives. Otherwise, as I said, if you find that you often leave a PD with less lives than you entered it with, also don't enter it.
Once you've beaten the boss once, I would go to Nightmare Mode and once you unblock

, you may go and unblock the remaining controllers and keys.
Good videos for that purpose can be found in the "TV Hammerfest" thread.
After you've beat the boss you can try out the 2-player mode and go for the

. Collect it 2 times and you will get a good advantae in 2-player mode in the future.
Also, if you want to post a link, please use the link tool. It makes your post nicer and it is easier to click the link

