You will need to obtain all 7 emeralds in one playthrough of the game.
Some things you can do to make this easier, is set the single player to Sonic alone, not Tails alone because Tails cannot turn into Super Sonic and there are 2 trophies for that.
The reason I say this is because having Tails with you on the special stage makes it a lot harder, because he moves/jumps out of the way of bombs too late. It's ok if he doesn't have any rings but sometimes he collects some stray ones which slip by you and it would be inevitable that he would later make you lose the bonus stage because he hits a bomb and loses you up to 10 rings.
Whenever you collect 50 rings or more and keep them until you pass a star post in the game (which is the checkpoint you start again from, should you die), there will be a ring of stars spinning around above the star post and will get wider and wider. You need to jump into this ring of stars when it stops getting wider. This will take you to the special stage.
In the special stage, there are 3 parts to it and you need to obtain a set number of rings in each section to pass onto the next section. If you fail to get the required amount of rings then the special stage will end and you will not get the emerald so you want to avoid this.
If you pass all 3 sections by getting the required amount of rings then you will get the emerald.
You can abuse the save feature in this game to help you out a ton with this trophy. You just need to press start at any time and Save. The save feature saves the exact moment you're at when you saved so it's technically a snapshot save.
It's recommended that you use a few save slots and save at the following moments:
1. Just as you jump into the ring of stars.
2. Whenever you get the required amount of rings to pass the section.
3. On obtaining the emerald.
The ring and bomb layouts are always the same so it's just a case of memorising where the rings come.
Bombs tend to come in groups and are usually able to be navigated around, there are a few instances where you will have to jump to avoid them.
Sometimes rings will appear to be above you but to get them you need to press hard left or hard right to get them, think of the stage of a giant tube and you can walk on the ceiling of it for a brief moment if you go up the sides very fast. You should never jump to get rings, none of them require jumping to get.
If you fail a stage then you will get put into the same stage you just did next time you collect 50 rings and get to a star post. You cannot use the same star post multiple times.
It's easier to get the emeralds in the first 2 zones so I'll detail locations. You must do these in order because activating a later one will also activate star posts before it.
Remember you will need to re-collect 50 rings each time, but the rings respawn after each special stage.
Now there are 3 star posts in Emerald Hill zone act 1.
1. The first one is high up early in the level, there is a slope which you will have to spin dash to get up and there is a spring at the top. Use the spring to get up to the left and there is a star post.
2. The second one is the obvious one in the middle of the level after the log bridge.
3. The third one is high up later in the level, it is after using 2 diagonal yellow springs, you'll need to use the vertical yellow spring to bounce up on the green platforms, the star post is on top of the loop platform.
4 in Emerald Hill act 2. (although one is very hard to get to)
1. When you reach the horizontal travelling green platform, take the upper platform. After crossing the log bridge and going down the slope, there will be a slight drop onto a platform with a spring. There is a green platform to the upper right that is going up and down. After getting on this, there is a spring on a platform to the right, you can use this spring to jump up to the left and getting the star post.
2. This one will be found if you follow the lower path after obtaining the previous star post.
3. This one is the bugger to get to, you may choose to skip this one if you prefer. You need to use the red spring marked at "5" on the map. You'll need to land next to the Shield item box on top of the loop platform. There will be a yellow spring at the right end of this platform and will take you to a platform with an extra life on it, the star post is on the next platform down to the right, be careful with this jump.
4. This one is easy to find, it's just a jump down from the previous one to the right. It's impossible to miss this as you need to pass it to get to the boss fight.
3 in Chemical Plant Act 1 - It's very easy to pass all 3 of these.
The 2 at the bottom of the level are the easiest to get to, make sure you bounce off the red spring and go through the tunnel system you arrive at. You should come out to the bottom right, this route will take you to the first star post. Where the map is marked "2", you need to turn around and go the opposite way and you will go all the way back to the star post.
The next one is a bit further on from "2" on the map, make sure you drop through the flipping platforms and it's on the left.