This has been one of my all time favorite games since release day. I was 17 years old when I bought it for the AES, and I just picked it up for MVS last month.
I can get to the last level without dying on default MVS settings. If you have specific questions about strategy or how to overcome certain obstacles I can answer them.
Here are a few all around strategies:
1. Never pick up the green bombs (missiles). They suck as a "save your ass" bomb, and the other ones are there for the taking anyhow.
2. The main weapon works best against bosses as a pulse cannon. In other words, don't wait for a fully charged blast, and don't just rapid fire. Instead, hold the button for a fraction of a second for a timed mini burst, release, and then immediately press it again. It takes timing but you should be able to get it down in a few minutes or so. You will make much shorter work of many bosses like this, especially the crab.
3. Bombs will appear at fixed points in the game, but only appear depending on what you already have in your inventory. For instance, in level one, if you use your fire bomb before going through the gated area(the one where you have to spin the turn-style to open the walls) another fire bomb will be waiting on the other side of those walls on the left hand side. So if you haven't used a fire bomb before that, you basically saved it for nothing.
4. If you think the crab is tough, just sell your cart now. The level 4 boss takes the difficulty to a whole new universe.
5. Boss one - If you time a fire bomb to strike him right as he is retreating from his forward rush attack, the boss will be stuck in the flame as he walks backwards. If you time it right it will kill him. One shot and done.
6. Boss three - If you are having trouble dodging his phase one bullets, make sure you have two bombs when you get to him (not the green ones). They leave you invincible, and after the second one he should go to phase two which is much easier.
7. Learn to use your side attachments as weapons. They cannot be harmed, they do damage when they strike things, and you can block projectiles coming from the side with them.
Everything in the game has a strategy/pattern/tactic associated with it. If you need help with a specific area, let me know and I can walk you through it.
~Anselm~