Maybe this will help. First you need to make lots of money. Second, you buy the fish environment research you can afford. You start in level 1 environment and there are 3 levels of environment. In level 1, only the level 1 fish will thrive - level 2 fish will die eventually and level 3 fish die as babies. Once you have level 3 environment, you can start some serious breeding and your fish won't die.
So to start, how to make money?
You start off in a level 1 environment. Until you get a breeding pair of greenfin spotanus (one of the most expensive level 1 fish), you should only breed fish that are identical - level 1 fish purebred offspring will be healthy and won't die - and you can sell those off for some starter money - so for example, breed a pink shark with a pink shark, twinfin spotanus with twinfin spotanus, etc.
How to find greenfin spotanus to sell?
In the first free batch of eggs, I see if there's a greenfin spotanus. If there's 1 or none, I use the starter money to buy a batch of common eggs and see if there are any in there, as it is a rather common fish.
Currently, I had 1 greenfin spotanus in my starter batch of eggs. I crossed different spotanuses (from the breeding guides) until I got a second greenfin spotanus. I sold off the other fish. With the 2 greenfin spotanuses, I bred lots and lots of greenfin spotanuses (also, if there's a greenfin spotanus in the tank, each fish will have 2 babies, not just 1). Then I quickly sell the greenfin spotanuses for $85 each while breeding more. This way, you can easily make tens of thousands of dollars to invest in fish research, food research, advertising research, etc.
With the upgraded fish environment, level 3, I buy a batch of common fish and breed my way up to the fancier level 2 and 3 breeds and they survive. Of course, it doesn't hurt to buy the other supplies, either.