Complete a Super Skill shot
To do this, you first have to make a regular Skill Shot. At the beginning of each ball the display shows a snake in one of three baskets, corresponding to the three holes at the end of the plunger lane. You need to shoot the ball into the hole that matches the basket with the snake in it. The farthest one is generally the easiest (just plunge as hard as the game will let you.)
After the skill shot, the ball goes down the ramp to the right flipper. If you make the skill shot, you can then make the Super Skill Shot by immediately shooting the ramp from the right flipper.
Collect the Jackpot during Genie Multi-ball
To start Genie Multi-ball, you must hit the genie enough times to light the locks (indicated by green arrows around the loops. Once lit, shoot balls into the loops to lock two of them, then you'll be instructed to hit the Genie to start multi-ball.
During multi-ball, all you need to do is hit the genie once to collect the jackpot. Additional jackpots can be collected by shooting a ball through the loop from either direction, then hitting the genie again.
If you lose two balls before getting the jackpot even once, you'll be given 10 seconds to shoot the ball into the bazaar for a rematch. This gives you another two-ball multiball and another chance to get jackpots.
Score a Fireball Award
Shooting the ball up the ramp advances you towards the next fireball. After 2-4 times an animation of the genie shooting a fireball is played and a score begins counting down rapidly from a value of 200K-1M. Hit the genie before this reaches zero to collect the points and this goal.
Capture a ball with a Shooting Star
You'll almost definitely get this without even trying, but to explain: There are two targets that light the "shooting stars" which catch balls above the inlanes to prevent them from going down the outlanes. 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. They only stay lit for a limited time, but it's long enough that it's not uncommon to get them without even trying.
Activate Harem Multi-ball
When the locks are not lit, Genie multi-ball is not active, and the left tiger loop target is not active, a white arrow will be lit at the left loop. Shooting the ball up the left loop when this is lit gives you a letter in the word HAREM, and collecting all five letters starts the Harem multi-ball mode.
This is probably the most difficult of the five standard goals. The best advice I can give is to shoot at the left loop often, and practice making that shot. Learning to hold your ball on a flipper is helpful too, so that if the time-limited tiger loop arrow is lit you can just hold the ball on the flipper until it goes back to being for the HAREM letter.