Relixander
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Typically, a medium sized creature does not actually occupy the entire 5' cube of space. This is also true (perhaps more so) when creatures get larger, a large creature does not usually completely occupy 10' cube of space, the additional space is provided for other game mechanics.
Typical ways to go through enemy square include (but may not be limited to), acrobatic movement, bullrush, overrun, the fact that climbing is involved may change what is available to certain creatures.
Titania, the Summer Queen
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I would make the DC to get past the large creature the same as it would me to jump over it. At least if the acrobatics skill was used. Since you can't overrun (charge) while climbing, I would rule that out.
Unless they have an actual climb speed of course.
For acrobatics( jump) I guess a DC of 60 would be sufficient .15 feet to make it into square above the large creature.