Yeah, I got this idea from another thread. So, the DC to jump straight to the moon is a minimum of... 356000 * 4, which is...


1425600

But, where there's a will, there's a way! So, here we go.

We're going to choose Wyvaran as our race, with Vestigal Wings, for the Acrobatics bonus. Now, since they get a +2 DEX and +2 WIS, we're going to choose Ranger as our class, for the synergy with these bonuses.
Here are our skill ranks + stat layout:

STR 10 / DEX 19 / CON 11 / INT 8 / WIS 16 / CHA 7

Skills:
Acrobatics
Knowledge (planes)
Jump

Since we get 10 feats over the course of 20 levels, I'm going to pump all those into jumping really, really high, and we'll take 12 levels of Ranger for max Jump bonus as well as the Burst of Speed spell. We'll also take some levels of Ninja for Ninja Tricks, two of which caught my eye:
Acrobatic Master (Su) (Ultimate Combat pg. 14): As a swift action, a ninja with this trick can focus her ki to grant her a +20 bonus on one Acrobatics check of her choice made before the start of her next turn. Using this ability expends 1 ki point from her ki pool.

PFS Legal High Jumper (Ex) (Ultimate Combat pg. 15): When a ninja with this trick makes a high jump, the DC for that jump is half the normal DC. The ninja must have the acrobatic master trick before taking this talent.

We'll take four levels for two tricks. Lastly, we need more movement, so we'll dump the last 4 levels into Monk (Unchained).
Feats:
Jumper, because our creature type is Dragon (always have running start)
Run for more jump (+4 after run)
Wind Leaper (activate for rounds, +1/2 Planes ranks to acro)

Traits:
Cliff Jumper (+1 acro)

and I couldn't find anything more, but we need the following magic items:
Boots of Striding and Springing (+5 acro, +10 ft)

So what does that all add up too? I'm sure I've forgotten something, but here we go:
50 feet speed, for +8 acro
Vestigal Wings, +2 acro
20 ranks acro (+3), +23 acro
Burst of speed + 10 speed, +4 acro
Jump +30 acro
Cliff Jumper +1 acro
Boots + 5 acro, +4 acro from speed
Acrobatic master + 20
20 ranks Knowledge (planes) for +10 acro (wind leaper)
High jump DC/2

for a total of...
DC 712800
Max jump height 8+2+23+4+30+1+20+10 = +98 jump, or 24.5 feet on a 1. We can jump extremely high, Mario style, but can't quite get it. But odds are, I forgot something.