Thanks for the question. I understand you are having issues with your Birthday calendar in iCloud, specifically duplicate events. The following article addresses Birthday calendar troubleshooting, and steps to resolve any duplicate entries:
To clean up issues related to manually adding birthdays to a calendar in Calendar (or iCal):
1. If you already have the Birthdays Calendar enabled, deselect it in the Calendars list in Calendar (or iCal).
2. Search Calendar (or iCal) by entering "birthday" (without the quotes) in the Search dialog in the top-right corner of the Calendar (or iCal) window.
3. Sort the Search results by title, so they are easier to analyze.
4. Locate any birthdays that are returned in the Search results that are not contained in a Holidays Calendar (such as John F. Kennedy's Birthday, Lincoln's Birthday, and so on).
5. For each non-Holidays birthday returned, decide if you want to keep it. If so, open Contacts (or Address Book) and verify that you have a Contact for the individual. Enter the birthday information for that person in Contacts (or Address Book). For more information about updating Contacts (or Address Book) fields, see this article.
6. After verifying that the birthday is entered in Contacts (or Address Book), remove any birthday events not stored in the Birthdays or Holidays calendars by selecting them and choosing Delete from the Edit menu.
Note: You can select consecutive items by holding down the Shift key while selecting them. You can select non-consecutive items by holding down the Command key while selecting them.
After cleaning up any manually added birthdays, you can enable or re-enable the Birthdays Calendar. To enable the Birthdays Calendar for the first time, open Calendar (or iCal) > Preferences and select the checkbox next to Show Birthday's Calendar. If you temporarily hid the Birthdays Calendar as per the instructions above, you can re-enable it by selecting the checkbox for it in the Calendar List.
This answer does not resolve the problem. I am having the same issue as the original poster (OP).
As with the OP, the problem is not with manually-entered birthday calendar events, but with iCloud Calendar's syncing with Contacts to pull the Birthday information (from the Contact entry - again, not manually-entered birthday events). Even though the information in my Contacts' information is correct, the Birthdays calendar is showing duplicates for every contact (with birthday info entered). And, like the OP, the Birthdays appear correctly on my iPhone calendar - they are showing duplicates in iCloud Calendar and iCal on my Mac.
How do we resolve this problem??
I have to agree with Aimsly. This suggestion does not fix the problem. I talked with Apple Support a couple of days ago and they too could not figure out why this was happening. They opened up a case and escalated it to their senior support. They are supposed to call me back by this friday. I've tried anything and everything I could possibly think of to troubleshoot and nothing has worked. It seems like iCloud Calendar has gotten stuck with a previous sync of my older iPhone(s) I no longer have. Will be waiting for a solution.
Hey, I have had this problem for the past week or so and I decided to just fool around with it since I have everything backed up already.
What I did was delete my iCloud account completely AFTER I made sure that all of my events, photos, contacts, etc were in the cloud AND on my iPhone 4s AND my MacPro. After that it you can delete your account and it will ask you if you're sure about 7 times because of all of the files and you have in the cloud and on your computer.
Once you're 100% sure that you don't want things on your computer you will be clean of your iCloud account and any duplicates.
After that I looked at my Contacts and I found I had duplicates or triplets of almost all of them. Of course this was a pain in the *** to delete all of the duplicates, but if you press Command and select all of the duplicates you can get rid of them really fast.
You'll notice (if you have Calendar open) that those pesky duplicate birthdays go away, but that all of your events are gone. OH NO!!! Don't worry.
Once you've done the first 2 steps you can now sign in to iCloud again and RESTART your computer. If you don't restart you won't see a difference in Calendar.
I hope that this helps anyone out there having the same problem.
All in all it took me about 30 minutes to do just experimenting, so it shouldn't really take you that long now that someone already did all the work for you