This is probably going to be one of the last trophies you unlock in the game given it is very time consuming, takes a lot of coins and a lot of luck.
You need to have one of every plant growing in your gardens at the same time.
You begin when you get given the Zen Garden but need to buy the Mushroom Garden and Aquarium. Periodically through the game you will get gifts that open to up to show themselves as new plants for your garden. You then need to go to your garden and water, feed, clean etc your plant until it's grown. It seems to count it towards the trophy once you have applied the first growth bag to reveal its identity. You can then purchase a wheel barrow to move it to the relevant area as all plants automatically start in the Zen Garden. You should also sell any duplicate plants you have to keep your money increasing (as you'll need a lot of plant supplies) and keep free space in your Zen Garden for any new plants you find.
There are 39 plants in the game you need to find (doesn't include the plant pot or upgrade plants). Three go in the aquarium - Lily pad, sea-shroom and tangle kelp, eight go in the mushroom garden - puff-shroom, sun-shroom, fume-shroom, scaredy-shroom, ice-shroom, boom-shroom, hypno-shroom and magnet shroom and the rest in the Zen garden.
Once you have finished the game, the mini-games and survival missions you will have most of them and the best way to farm the missing plants is to repeat the hard survival missions. There are five types of level and each level corresponds to a line in the Almanac so you should farm the relevant survival mission for the plants you need.
1st Row - Daytime levels - Peashooter, sunflower, cherry bomb, wall-nut, potato mine, snow pea, chomper and repeater
2nd Row - Night levels - puff-shroom, sun-shroom, fume-shroom, scaredy-shroom, ice-shroom, boom-shroom, hypno-shroom and grave buster
3rd Row - Pool levels - lily pad, squash, threepeater, tangle kelp, jalspeno, spikeweed, torchwood and tall-nut
4th Row - Fog levels - sea shroom, plantern,cactus, blower, split pea, star fruit, pumpkin and magnet-shroom
5th Row - cabbage pult, kernal-pult, coffee bean, garlic, umbrella leaf, marigold and melon-pult