You can play limited time missions once a day, or even more frequently at times, and sometimes even multiple missions per day. During these missions you will find a flood of gems compared to your usual missions. Gems are the primary currency in the game (the blue squares that pop up). Credits are the gold currency that pop up during the game.
Typically you will only earn more credits for free when you beat a boss for the first time, so save the ones that you earn and use them for better than just restarting after you lose a stage. Go to the black market and you can spend three credits at a time to earn a rare piece of equipment. Or, after you beat the limited edition stage, you’ll often have the opportunity to get a rare cargo box for just one credit.
If you are having trouble on levels, the best way to improve your chances (aside from improving your skills at the game) are to improve your equipment. In addition to the equipment that you earn from cargo boxes, spend gems in order to upgrade it. Each piece can be upgraded from level 0 all the way to level 5 at the max, costing an increasing amount of gems every time.
The main statistics to consider are damage, armor and health, with damage representing how much damage you do to enemy ships when you shoot them. The rare equipment not only has higher numbers for statistics, but it also has multiple stats that it boosts at the same time. Improve the rare equipment with your gems as that’s typically the equipment that’s the hardest to replace.
Also look out for equipment that gives you an extra auxiliary shot, whether it’s rare or not. Usually this will happen as a secondary characteristic and by itself it won’t have much of an effect. However, stack one or two of these together, and combine that with upgrades, and you’ll start to look like those kids who were really good at Raiden II in the arcade back in the day (I.E. be launching so much firepower that you’ll barely be able to see what’s going on).
Sometime around the third chapter you will unlock the ability to purchase new ships. All of the new ships cost credits to buy, making this the best thing to save your credits for outside of the rare cargo box (and even in addition to the rare cargo box). New ships will typically have new weapons as well as bonuses to statistics, extra shields, and secondary weapons that often include debuff characteristics (such as paralysis due to electric shock).