Jumble Hopper Shortcut:
First, you must get to the third stage of the Jumble Hopper event. When you begin this stage, jump between the building you start on and the building in front of your starting position. The aim is to get through the doorway of the bluish-green building. This is best done by jumping against the building across from it, and landing right next to the open doorway. This is very difficult to do and requires a lot of practice. Once you have mastered this, you will be able to jump into the hallway (with much difficulty) and follow the path until it leads out into the street. Once you reach the street, you will notice that you have warped into New York. This is not very far from the goal. If you are good enough, you will be able to get a near-perfect score (depending on how many points were taken off during your journey).
Cannonball Tips:
While the following numbers are guaranteed to get you inside the bull's eye, you may need to make some minute adjustments to ensure a rating of 25 points on each shot. Also remember to recalibrate the cannon after every shot. Just leaving the cannon on your last setting and firing a second time will result in an even lower score than the previous attempt. While most of these shots are calibrated for full power, some require less. In these cases, a little trial and error will get the best results.

Symbol Key:
V = Vertical
H = Horizontal
P = Power

ROUND ONE:
Cannon 1
V:1-2 degrees
H: W 50 degrees N
P: Full
Cannon 2
V: 12 degrees
H: S 70 degrees W
P: Full
Cannon 3
V: 18 degrees
H: W 30 degrees N
P: Full
Cannon 4
V: 4 degrees
H: S 87 degrees W
P: Full

ROUND TWO:
Cannon 1
V: 10 degrees
H: S 65 degrees W
P: Full
Cannon 2
V: 5 degrees
H: S 12 degrees W
P: 1/2 (a little less)
Cannon 3
V: 29 degrees
H: W 28 degrees N
P: Full
Cannon 4
V: 18 degrees
H: E 49 degrees S
P: 3/4

ROUND THREE:
Cannon 1
V: 13 degrees
H: E 23 degrees S
P: Full
Cannon 2
V: 7 degrees
H: S 85 degrees W
P: 1/4
Cannon 3
V: 52 degrees
H: S 41 degrees W
P: Full
Cannon 4
V: 45 degrees
H: E 54 degrees S
P: Full (a little less)
Birdman Transport:
Using any of the vehicles in the first level, you will find a bridge-shaped rock formation with a giant golden star under it. Go to it, hit it, and you will automatically transport to the birdman level.