Finished my write-up of my high score technique. Sorry this is super long, but maybe this is helpful info!
The most important thing to learn is turtle tipping/beetle bopping, which is the act of continuously jumping on and kicking turtles back and forth against a pipe or a block. In general, the highest scoring strategy I could find is rushing to the best spot in each level, turtle tip, and then rush to the end with as little time remaining as possible. Ideally you want to finish each turtle tipping level with 6 seconds left on the timer for the maximum fireworks bonus (3000) while hitting the top of the flagpole each time for 5000 points.
The 10-coin blocks are also quite lucrative and are worth seeking out, especially if you are big Mario and can empty them efficiently.
Try and keep a fire flower equipped for the Bowser fights for an easy 5000 points. Take your time and grab all the coins and powerups. No need to rush here.
I break down turtle tipping into two separate categories: Tipping against a single wall, or in between two walls.
For a single wall, the priority is to avoid losing the turtle. My technique was to focus on stomping the turtle and then backing up off the bounce a tiny bit just to ensure I can aim the turtle back into the wall. Then repeat ad nauseam. This method took the most practice by far. If you really want to squeeze out points, try to minimize the distance between Mario and the wall as much as you feel comfortable. I started out keeping 5-6 blocks of space and narrowed it down all the way to about 3.5 blocks. I used to get around 70K-80K in 1-1, and I pushed that up to 100K a few times by tipping very aggressively.
For turtles in between two walls, the technique varies a bit depending on how many blocks of space you have. Three blocks space is too dangerous, I never bothered! Four or five spaces is ideal. Just get all the way to one side and work on timing. With 6-9 blocks of space, stand in the center and tip. You don't have to worry about aiming the turtle at all, and you can earn points really fast in the narrower spaces. (I will caution that the six space spots are really risky and you have to hop almost immediately after hitting the ground. I think there is only one of these in the game though.) For ten blocks or wider, I had better luck being aggressive with the single-wall method and using the back wall to help recover any shells you let go by. Or you can stand in the middle for a safer method that yields fewer points, your choice. Actually you can use either method relatively safely on nine space sections.
Here are the turtle tipping spots I found:
1-1
Tip the only turtle against the right pipe. Two tips: If you want to grab the ?-block coins while chasing the shell, only grab the first two. The third coin block sometimes causes one of the goombas to not spawn, costing you 5000 points. The second tip is to stop the shell off the rebound and break the two lower blocks so that you can narrow the distance to the pipe. It pays off to be aggressive here since you can just reset if it doesn't go well. I left 30-35 seconds on the clock before rushing to the end.
1-2
Tip the first/second turtle off the left wall. Be careful not to kick both turtles left or you will lose both. This spot is tricky because it is the only spot worth tipping off a single left wall, and sometimes you can scroll too far right and can't see the wall, which really throws off my timing. If you lose the turtle, try and chase it right to pick up a few extra points. I could have been a little more aggressive maybe, but I left the spot with around 100 on the timer.
1-3
Tip the last turtle against the stairs at the end. I usually played it safer here for more guaranteed points, especially if I had a strong 1-1 and 1-2 so as not to completely blow it. 18-20 seconds left and you're good.
2-1
Two good spots here. The first is the first set of turtles between the two pipes. Reveal the hidden coin slightly left of center so you don't accidentally hit it, and stand in the middle one space to the right to tip. You can leave 120 seconds here, and I took the vine into coin heaven. The other spot is the final turtle near the springboard. I liked to use the "wide two-wall method" and tip off the springboard only with the left pipe for recovery only. Or you may want to play it safe and keep the fire flower for 2-2.
3-1
Just before the bridge, there is a turtle in between two pipes with a lonely brick hanging out. This is a really good spot to turtle tip by standing in the center. If I had fire power, I left 90-100 on the timer before moving on, otherwise, you may want to leave early to make sure you can make it past the Hammer Bros. You can also earn a boost of points with the mess of koopas and goombas at the end of the stage. If you tip the shell after colliding it with enemies, it keeps the point bonus and you can grab up to 8000 points off the final paratroopa. Naturally, leave the stair turtles alone or just fire them!
3-2
There are three spots here, and I think it's a good idea to tip at the first available spot and move on if you lose the turtle. You can tip the first turtle, the turtle in the next section, and the final turtle. Do not tip the second-to-last turtle or you will despawn the last turtle and lose the normal points. The middle section is good because you can keep the left wall in play for recovery if you don't scroll too far right.
4-2
Either the turtle or beetle near the tallest pipe are your best tipping spots. I liked to nuke the turtle and empty the 10-coin block before tipping the beetle on the other side. You can leave 90-100 seconds here, depending on if you want to grab the powerups and coins on the way to the end. There are many spots to exploit for points if you need to move ahead and grab a powerup for safety, but the beetle is by far the most lucrative tipping spot.
5-1
All the spots are good here. I most prefer the paratroopas at the very end. You can scroll the bullet bill cannon off screen and tip against the staircase. The cannon won't shoot when you can't see if but the wall remains for shell recovery purposes.
5-2
The best spot is the first turtle between the stairs and springboard. I never jumped high enough to worry about getting hit by the bullets. I normally left 140-150 on the timer, but I could have been a bit more aggressive and gotten away with it, particularly if I had firepower. I also never exploited coin heaven here, so that could yield slightly more points
5-3
Same as 1-3 with the final turtle. This can really hurt your score if you lose the turtle, so just be careful!
6-2
The first paratroopa is the best tipping spot here, but the problem is the piranhas cause it not to spawn very often. The next best spot is the second beetle, the one past the really tall pipe. I left around 90-100 on the timer but I think I could have maybe cut that down 15-20 seconds if I really wanted to be aggressive. You can tip any of the other shells past that point in the level, but I never bothered.
7-1
There's an excellent spot here that requires some careful setup. Past the first set of Hammer Bros, there is a turtle in between two pipes. The trick is to gently scroll the screen forward just enough to remove the left cannon, but not too far so that you don't introduce the right cannon into view. I think the sweet spot is inching up to about the second space in between the pipes, then back up and tip while up against the left pipe. You can be really aggressive and leave 30-40 seconds on the timer before leaving if you have a fire flower to dispatch the Hammer Bros and can skip that powerup at the end of the stage. I recommend practicing this spot ahead of time because there are a ton of points at stake here.
8-1
There are a lot of single wall spots here that are safe to tip. I usually got the beetle in between the two pipes with the 1up. Here, tip on the right side so that you don't accidentally bop the 1up block when trying to make your escape. I left with around 150 on the timer so that I could take my time with the rest of the stage, and then I tipped the last turtle until around 25-30 so that I had enough time to clear the stage.
8-2
The final beetle is the spot here. Stand against the cannons on the right to keep them from firing. You can quit with around 20 left on the timer and still make it fine since it's at the tail end of the stage.
8-3
This is the last spot I found, and like 7-1 it takes some setup. Past the first set of Hammer Bros, there is a paratroopa in between the cannon and the wall. First, bop the koopa so that it doesn't hop over the cannon and you lose it. Then scroll the screen forward enough to remove the cannon. You can quit with around 70-80 on the timer if you have firepower.
8-4
In the second section of the level, you can tip either the beetle or the paratroopas in between the pipes. A word of caution: If you choose to tip the beetle, eventually the paratroopa will come over from the right and get involved. Tip until time runs out, since beating the game isn't required! Bea said you can earn more points by carefully kicking all enemies while looping the section over and over. She is probably right, but I didn't bother experimenting with that if I managed to get to 8-4 on a single life!
