First, you'll need to have completed all the basic goals for the basic goal achievement. The wizard goals do not unlock until you complete the game in which you finished the basic goals, and won't be marked as completed if you've accomplished them before then.
Win the Great Camel Race
The camel race is one of the seven jewel-earning modes that start by hitting the genie when no special modes (fireball, multiball, etc.) are active. You can control which mode starts by looking at the set of seven lights just above the flippers; one mode will be flashing and each hit of the left flipper button cycles the flashing light to the next mode that isn't lit (already completed). The camel race is the 5th light from the left.
Once the camel race is started, you advance ahead in the race by hitting any of the four flashing yellow targets: A target on the left side of the table underneath the left loop, a target to the right of the genie, and both the loops. The targets don't change and can be used multiple times. I find the left target is easiest to hit repeatedly: Hold the ball with the right flipper, then let go and hit it again when the ball has rolled about three-quarters of the way down the flipper. After hitting any combination of four targets, you'll have advanced to first place and the goal will be unlocked.
Note that while the race continues even if you lose a ball, you have to reach first place on the same ball you started the race on, or the goal won't unlock.
Collect 60 Lamp Spins
Lamp spins are accumulated by hitting the lamp hard enough to spin it around during regular play. Every 15 lamp spins activates the lightning lamp mode. Lamp spins don't accumulate during the lightning lamp mode, so you should hold the ball on a flipper and just wait for the lightning lamp timer to run out (as the time resets every time the lamp is spun during lightning). Upon activating lightning lamp for the fourth time you should have your 60 lamp spins.
Note that lamp spins do not accumulate during multiball, and reset to the last multiple of 15 you reached when you lose a ball.
Collect the Ruby
The ruby is lit by getting both the left and right shooting stars activated at the same time. The left shooting stars are activated by hitting the target underneath the left loop, and the right shooting stars are activated by hitting the target to the right of the genie.
Shooting stars only stay active for a few seconds after they're activated, so you need to hit one of these targets then quickly hit the other. The best strategy I have is to hit the left target with the strategy mentioned under the camel race goal, then quickly pass the ball to the left flipper and shoot the ball in the direction of the lamp; if the lamp is aligned right the ball will pass between the two posts underneath the lamp and hit the targets to the right of the genie.
Earn an Extra Ball
The easiest and most reliable way to light the extra ball target is to collect any four jewels, which you'll be doing on your way to the Rescue the Princess goal anyway. Once you've done that, a dark red arrow will light at the right loop; shoot the ball up there to collect the extra ball. Note that the extra ball target can also be lit by getting six tiger loops or as a random award from the bazaar.
Rescue the Princess
First, you'll need to collect all seven jewels. The easiest way to get jewels is from Make a Wish. Each time you activate lightning lamp (spin the lamp around 15 times, not during multiball), Make a Wish will light. Shoot the bazaar target and you'll be offered the choice of one free jewel (two if you have the ruby) or one of several other awards. Take the jewel, spin the lamp again, and repeat until you have all seven jewels. (Alternately, you can earn the jewels by completing the jewel-earning modes which start when you hit the genie outside of multiball or fireball modes. Note that if you're in the middle of a jewel mode, collecting the jewel from Make a Wish will end the mode and give you the jewel you were working on, so you should avoid the bazaar so as to not waste a wish if you're close to earning one the natural way.)
Once you have all the jewels, hit the genie to start the rescue mode. Three of the five yellow targets around the table (located underneath the left loop, to the right of the genie, the ramp, and both loops) will flash. Hitting a flashing target or the genie destroys a skeleton, and the genie will replace it with another skeleton and another flashing target. After you've destroyed several skeletons they will stop being replaced., and when only one remains the lights at the left and right loops will flash. Shoot the ball through either loop to begin the second part of the rescue.
In part two the score display shows the genie on the left, you on the right, and the princess's bottle in the middle. The bottle will gradually drift towards the genie but can be pulled towards your side by hitting the five yellow targets and the genie target on the table. At the beginning of this mode you can shoot three more balls in play and any balls lost immediately go back into the plunger. You should always re-shoot any lost balls right away as you can hit targets more frequently with all four balls in play. Once you get the lamp all the way to the right side of the screen the genie is defeated, you get 20 million points for rescuing the princess, and this goal is completed.