Here is an alternative for those who have completed the game but don't want to travel/climb all the way up there.
When replaying memories, you can go to the Memory 2 in Sequence 8 called An Apple a Day. After the cut scene that occurs, you'll be placed near the top of the Castle. It cuts out the entire climbing sequence and you can easily get up the pole. However, make sure you've completed all of Leonardo's quests because you cannot get the achievement without doing so.