sfrose has written this guide, which provides one approach for producing all 6 Magic Plants from a specific set of starter plants.

Major Spoilers! This guide with help you take the right track, but I'm leaving some of the crosses that you need to make to experimentation.

Start with these plants:
Spotted Reptans
Citrus Reptans
Citrus Ball Cactus
Fourpetal Ball Catcus

It is possible to solve the puzzle with other starting combinations, this is only one appoach. The first thing you should do once you've verified that you have these plants is to self-pollinate them in order to save seeds to use later.

The next plant you'll need is (you may have already gotten this in your initial seeds/plants):

Jalapa Maranta

From these five plants you can make your first Magic Plant:

Fourpetal Maple

And then your second Magic Plant:

Rosaceae Fern

At this point you may want to self-pollinate your Magic Plants to save for the soil upgrades.

The next plant you need to make is (you can do this with one cross from the above plants):

Fragrant Maple

With this and another plant you already have you can make your third Magic Plant:

Fabled Lemonbush

This plant will help you earn more money for more upgrades.

Your fourth Magic Plant is also available from a simple cross of the above plants:

Nox Orchid

If you haven't upgraded to Level 3 soil, you'll need to be careful about keeping this plant alive.

For the next two Magic Plants you'll need to make the following plants:

Fragrant Grass

and then

Aureus Fanleaf

Each of these plants, plus one other that you already have will create:

Aureus Scandens
Mela Rare Oak

Good Luck!