Ahhh...Tempest tips. This subject comes up every so often...always happy to contribute.
Background for me: Tempest was MY game BITD. It was my mission to get the highest scores possible at every location I could find one. My eventual high score was about 1.8 million on factory settings. My average game these days takes me to the 1.2-1.3 million

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Here are some the basic tips I would give for some of the things that players have trouble with:
1. Pulsars: All pulsars "pulse" at the same time. You will only die when you cross a lane with the pulsar below it in full "pulse" mode. "Pulse" mode is identifiable when a given pulsar is in full "accordian" or "ziz-zag" style (as opposed to straight), and is also accompanied by a bass-like sound. So to get them, you just wait until they are all in non-"pulse" mode, and then swoop in with your shooter and kill as many as you can. Note that pulsars can kill you when they shoot you and/or land on you as well (less common).
2. Flippers: What to do when the flippers reach the circumference/edge of a figure: Just wait for the flipper to flip to the lane immediately adjacent to your shooter, and then fire (with as few bullets as possible). That's it. As you improve, you can find space on the enclosed figures when 2 flippers are approaching from opposite directions where they will reach your shooter simultaneously, and then fire and you'll get them both! On non-enclosed figures, pick a side and let the flippers come to you.
3. Other flipper strategies: For some figures, observe the angles at which the flippers reach you after they reach the figure's edge. Let's use the "Star" figure as an example. If a flipper is headed your way, choose a side of this figure to sit your shooter at whereby the flipper must flip more than 180 degrees before landing on your shooter versus a side where this angle would be less than 180 degrees. The more time you have before the flipper lands you, the more time you have to kill it. This also works wonderfully on the figure that is shaped like an infinity symbol (the last shape before entering the next color). I always do as much damage as I can from the left side of this figure as the flippers must travel almost a full 360 degrees before killing you so you have much more time to kill him first. You do have to master the reverse motion for this side however

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4. Do you know what your tanker will split into? Look in the circular center of any given tanker on the later levels. If you see a line in there, this tanker will split into 2 pulsars on adjacent lanes when hit. If you see a squiggly shape in there, it will split into 2 fuseballs that will likely travel up the adjacent lanes and kill you if you don't move fast. If the center of the tanker is otherwise empty, it will split into the usual 2 flippers. Learn to spot these clues as it will help immensely on the later levels, particular from the yellow levels onward.
5. Watch the motion of the flippers as they travel up a given figure. This motion is very "figure-dependent." What I mean is that on some figures (such as the circle), the flippers travel straight up the figure and do not deviate into other lanes. On the square, they proceed in a circular motion up the figure (changing lanes all of the way). On the 4th figure (kind of looks like a peanut), they travel outward and then inward as they make there way to the edge. These motions are very good to know by heart as it will help you to know how best to spread your firepower.
6. Save your superzapper! Always, always, always save your superzapper until a given figure is nearly completed! You can tell if you are almost done with a figure by observing the tiny red dots at the bottom of the tube...when most of these are gone, you're almost done. If you use your zapper too early, you risk being surrounded by bad guys towards the end of a given figure, particularly fuseballs that will kill you and you'll have no way to get them. You can lose several shooters very quickly in this way if you're not careful. Also don't forget that you have a second zapper per figure that will get one enemy only. This is VERY critical in later levels when there is just one fuseball left that will track you down very quickly while you're waiting for the rest of his "friends" to finish their journey up the tube so you can jet to the next level. The second zapper will almost always take out this last fuseball.
7. Killing fuseballs: Learn the timing motions of the fuseballs. They move up and down the tube continuously. In the later levels, they will usually move right to the edge when they first appear, sit there for a second or so, and then move back down. So you just first assume they will go right to the edge when they appear and move out of the way, and then swoop in to kill them when they move back down. It will take practice, but once you have this timing down, it will be easier to kill them en masse.
Really I should post a video of gameplay in action one of these days...
Hope some of the above makes sense...and I do hope that some of the younger generation will be able to master this game as we earlier generation players had so much fun doing BITD
Jon