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If you need to complete a quest in Krokotopia but can't get in, you'll need to finish the main quests in Unicorn Way, Triton Avenue, Firecat Alley, and Cyclops Lane. I (and lots of other people on this forum) highly recommend you do all side quests (including Collosus Boulevard) so you can level up and get better gear, stats, and health.
You have to finish Triton Avenue, Firecat Alley, and Cyclops Lane. Then Professor Ambrose will have a few more things for you to do. After you finish those, he'll give you access to Bartleby and Krokotopia.