Okay, first off. This is seriously difficult. Unless you are a god at Tempest, you are likely to struggle and you will need to get lucky. However, here are some tips I think may be useful and I am also going to link a video that helped me;
1) So first off, you don't actually need to play until level 81. If you activate cheat mode you can start at level 81. If you press options and go into game options, change the difficulty to easy and turn cheat mode on. Now you can select level 81 from the first screen by scrolling all the way to the right.
2) Find a sensitivity that works for you! I found the D-Pad useless for this game so had to use the Left Stick... but the default sensitivity was way too fast to be useful for me. I ended up settling at sensitivity 3, but find whatever works for you.
3) Hold down "X" to shoot at all times. I know this may seem a bit silly, but at first I was tapping the X button to fire. Holding the button down shoots a lot faster than you mashing, plus given how long you will be at this your thumb will thank you
4) You have a Superzapper, use it! The Superzapper can be used once and destroys a bunch of enemies on screen around you. In a perfect world, you would use this when the the screen was full of enemies, but if you are anything like me, there will come a point in the level where you are just a bit overwhelmed and can't follow everything on screen. I would use it then just to give me a couple seconds breathing space and to refocus.
5) I know it is tempting to either chase enemies in other lanes or run away from enemies across multiple lanes, but try to refrain from doing this. What usually ended up happening to me when I did this is I would either over/undershoot the enemy and die or get rapped between multiple enemies and die. I am not saying don't use all of the lanes, but I found it better to focus heavily on keeping about a third of the lanes clear and only moving into other lanes when I needed to. The video I have linked below shows a good example of this and it was after watching that video that I changed my behaviour.
6) Regarding the blue shock enemies. NEVER chase them when they first spawn. If you happen to be aiming at them when they spawn and kill them quickly, great! However, they seem to at random destroy (black out) the lane they are on. I would often die instantly if I chased them to their lane and found the best way to deal with them was to wait until they blacked out a lane then kill them straight after that, as there seems to be a cooldown on how often they can do that.
7) When the lanes flash rainbow colours, that means the stage is about to end. Given how chaotic things have been, you entire focus will be on the foreground. As soon as they start flashing, take half a second to adjust you focus to the background and see a lane that is clear of spikes and then get into it. Now, half a second is a long time in this situation and you may die on occasion as soon as you shift your focus, but better to know which lanes are safe from spikes before you start moving towards them!
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Note: the next 3 'tips' aren't really about the gameplay... but these are ones I want to pass on as mentally they put me in the right frame of mind and protected my sanity 8) When you first start trying this, you may find (like I did) that you cannot clear the level at all with all of your lives which leaves you feeling a bit hopeless. It seems to me that when you die in this game you do not come back to life exactly where you left off in the level. It seems that the level gets extended each time you die, plus there seems to be a surge of enemies after a death. Once you can clear the level you start to realise this and it becomes a bit more manageable. Also, you are likely to either waste your Superzapper too early or keep hold of it until you are already dead at first and this becomes more manageable.
9) The yellow box enemies that follow you around the lane are super annoying. Once they have hit the front of the lane, there appears to be two main ways to deal with them, You can stay still and rapid fire and they die before they touch you, or you can quickly zoom under them while they are moving. The problem I had is that I couldn't get either of these things to work consistently. I had to get lucky. What this means from a positive point is that on a bad run you might die quickly, but on a good run you could get lucky with this 3 or 4 times, which can make all the difference. Perseverance is key!
10) The above brings to my last point. Despite all the chaos, the level is only about 45 seconds long. This seems like a lot when you are in it, but on the plus side it means that you can really get used to it. After a bunch of retries, you might be getting close but just can't quite the seal the deal, then you get 4 lucky draws with the yellow boxes and are on a spike free lane when the lanes start flashing and BINGO! You are done. Obviously what you kill affects score, but for reference of how far you are getting, I got ~10,300 in the level and the guy in the video below gets ~9400. Always keep in mind that a successful run is short, even if it comes after hours of failure!
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See video below that helped me. I take no credit for the video and full credit goes Jeffrey Livingston who uploaded. I just found it on Youtube.
Good Luck!