This achievement has two parts to it:
1) Get the "Great Gospel" item through a small quest.
2) Obtain all of Aeris's other Limit Breaks through combat.
I will be going over the second requirement, as WayzoftheRaven's guide for the item you need is good. If you are looking for the item Great Gopel itself, check out their guide! If you are wondering how to level up Limit Breaks, this is for you!
As this achievement is missable, I chose to do this immediately after the events in Rocket Town. You must do this before going in Temple of the Ancients.
Here is a general sense of what you need to do to get Aeris's other Limit Breaks:
Level 1
1a) Healing Wind- You start with this.
1b) Seal Evil- Use Healing Wind 8 times.
Level 2
2a) Breath of the Earth- Defeat 80 enemies with Aeris.
2b) Fury Brand- Use Breath of the Earth 6 times.
Level 3
3a) Planet Protector- Defeat 160 enemies with Aeris.
3b) Pulse of Life- Use Planet Protector 5 times.
You can set the level of a Limit Break in the "Limit" menu. You can only use the Limit Breaks in the Level you set, so keep that in mind. That being said, you can change back and forth whenever you'd like, but it does reset your Limit meter.
Apparently, you do not need to get the second Limit Break in a Level to advance to the next. So, to get "Breath of the Earth", you don't have to use "Healing Wind" 8 times, just defeat 80 enemies. Seeing as how you need all of her Limit Breaks anyway, I would just get the 2nd Limit in each Level before working on the enemy defeats again.
For enemy defeats, just go to an area where you can one shot enemies. Aeris must get the killing blow, so just have your other party members defend if it's not her turn. If you have any moves that hit all of the enemies (such as the Shiva summon, earned through the story), use those. You don't have to do this though; I just used basic attacks to defeat everything. I would use the "x3 speed" cheat by pressing the Left Stick so this doesn't take as long.
"Using a Limit Break X amount of times" can be somewhat tricky, depending on what level you are. You can fill the Limit Meter by taking damage in combat. A great way to do this is to give Aeris the "Cover" materia, which can be found in the garden by Aeris's house. You can also buy it in Sector 6's Wall Market if you didn't pick it up while you were in the garden. Once you have this, use a "Hyper" item (found in most item shops); this gives Aeris the "Fury" status, which doubles the rate at which a character obtains their limit meter. Now, go find a group of enemies that do a good amount of damage to you. I was ~Level 30 when I did this, and I searched outside Rocket Town until I found a group of 3 of the "wolf" enemies. Use the "x3 speed" cheat again and let the limit meter fill up, healing as needed. Keep using the Limit Break you need as you get it and it's possible to get all of the uses done in 1 battle!
NOTE: If you don't feel like doing ANY of the above for "using Limit Breaks X amount of times", you can also just press the right stick to get instant Limit Breaks. While you could do this if you want, I find it not as fun to do, so I did a bit of grinding.
I hope this clarifies a few things!