This achievements works as advertised, but it does not track, so don't panic if you don't see progress going up.
For this achievement you don't need to get the highest score; anything that asks you to enter your initials will work for this.
The thresholds you need to hit are:
Tales of the Arabian Nights - 5,298,310
Theatre of Magic - 200,457,920
Ripley's Believe It or Not - 4,004,910
Black Hole - 102,810
Learn to use table bumps. If you press the left stick in any direction, you will strike the table, moving the ball in the opposite direction. When you get really good you can use this to influence which targets you hit, help out in the jets, even make some skill shots easier. But on a basic level, if you see the ball going straight for the middle and you don't think you will be able to hit it, just bump the table left or right so that it will hit a flipper instead. This will come in handy so many times, and keeping a ball in play always means more points.
Tips for specific tables:
Tales of the Arabian Nights: If you are able to reliably hit the genie and the ramp, you're all set here. A lot of big points opportunities rely on you striking the genie. Want to start multiball? Strike him to spell GENIE, lock two balls (the left or right loop will do this), and then strike the genie. Want to start a tale? Strike the genie, and at the end of the tale, hit the ramp to get a jewel. Fireball? Hit the ramp and then strike the genie quickly. Seriously, if you know how to strike the genie and the ramp, you're golden.
Theatre of Magic
Your main goal in this game is to get to the finale of the magic show by completing all of the illusions, among a few more objectives. You won't need to get to the finale to get a high score however. When you launch the ball you will see a number of options cycle on the screen. I would suggest always launching when you see "start illusion" and then attempt to hit the trunk immediately to get an illusion going. When you're not in an illusion, work on hitting the trunk to start a new one, or going into the ramps to work on getting the locks and multiball set up. This is not a high score so you should have it 2 or 3 illusions in, or after a multiball.
Ripley's Believe It or Not
Sorry, this table confuses the heck out of me. I've read all the directions and it still confuses me. The only tip I can remember is that you need to be able to hit the shrunken head reliably. Read the instructions first as different parts of the table have kind of weird names. Other than that all I did was keep the ball in play and make sure I kept hitting things.
This is my favorite table of the "core pack". Your main goal here is to rack up a nice bonus using the lower table. If you want to make this happen faster, the "g force" lights can be activated by spelling BLACK or HOLE using the drop targets by hitting letters in order. When you get down to the lower table, your first priority should always be opening the gate by hitting all the targets in the left bank or right bank. Once it's open, go nuts. Make sure you get a 5X multiplier going when you're on the bottom table by hitting the loop on the right. You can't see the loop, but you'll know when you hit it because you'll still be able to see the multiplier light up.