So first thing is first, deep breath and do not worry. Talespin is not nearly as hard as people say and not nearly as bad as people say. It is only the first level that is quite tough, thereafter the game gets easier with upgrades.
This took me 45 minutes and I only played the first 3 levels competently before diving in.
You need to ideally hit perfect on all 3 first stages which means you will collect all crates and moneybags - if you miss one - kill yourself and you get take back to the previous checkpoint.
Upgrades bought should go like this:
Rapid Fire
Super Rapid Fire
Enginge
Armour
Here are my tips:
1. You can only change direction when horizontal - remember this or you will die sometimes to silly mistakes!
2. You need to absolutely Ace the first level. You need to get a 'perfect' bonus which is for collecting all the crates and money bags. There is a bonus level in the part just before the waterfall, when you see Don Karnege there will be 4 crates to collect, shoot directly where they are and enter the bonus level.
There is a hidden money bag in the second cloud after the waterfall part, do not miss this.
When getting past the submarines, stay low and in the same position, let them fly up and towards you then shoot for a guaranteed hit. Be careful as if they drop a bonus item it might block your shoot so be ready to shoot twice to hit the next submarine.
Watch this and learn the level:
3. Enemies respawn very quickly when you back track - be prepared to kill the same thing twice if you go back.
4. You have a lot of lives and continues - don't sweat if you lose some
5. Most bosses are easy, study the video and be wary of your placement. The hardest IMHO was the Twin fighters, best thing is to wait in the middle of the screen and if they fire the green bulllets you can easily dodge by going to the bottom right and around the bullets.
6. If you have nailed the first 3 levels and have both Rapid Fire upgrades, it's a case of taking your time as soon you will have a lot of cash for continues.