Method 1 for R/S/E
Method 1 RNG can be quite annoying sometimes, because there is only one starting seed for both games (0 for Emerald, 5A0 for R/S) so waiting times can be several hours! So it may take several days to get your project done. But there aren't too many Method 1 pokes that get good exclusives. And in Ruby and Sapphire you can get good shiny legendaries with retail cart ID abuse. Remember, synchronize doesn't work with Method 1! Also remember, you need dead internal battery Ruby/Sapphire for this to work. Here's the small list what you should definitely RNG in 3rd Gen.

- Shiny in 3rd gen | Counter (This needs to be ID/SID Abused with an Emulator)


- Lvl 45 in R/S (Do ID/SID Abuse, because you need Ruby/Sapphire anyways)

- Seismic Toss | DynamicPunch | Counter (Method 1 Keckleons with Steven Scope) (Only if you want it in cool ball)



- Seismic Toss | Counter (You should go for shiny in R/S, because there are better spreads than in Emerald)
RNGing these pokemon is simple, but slow. They all have their own lag, and it can be hundreds of frames. You may need to adjust it to EonTimer. But otherwise it's fairly easy. Get your catching party ready, and go to your desired pokemon. Save in front of it (incase of Groudon/Kyogre, save one step before auto-move) and shut your game off.
Open up RNG Reporter. Stay in main window. For both games, select Method 1. For Emerald, leave your seed empty. For Ruby/Sapphire, your seed is 5A0, if your battery is dead. Search for good spread using RNG Reporters by IV Filters and selecting few viable natures. You should just do 28+ in all desired stats. Even then it may take tens of minutes waiting time. Once you have found your Target Frame, put that into EonTimers Target Frame. Now, in RNG Reporter right-click your target frame and select "Center to +/- X seconds and set as target frame." In place of X set good seconds range for you. If your target frame is over 40 minutes, you should just put it as 5.
Then you are ready to go. Start EonTimer, soft reset when first timer hits 0, then do your last input (moving to Kyogre/Groudon, A press for other) when second timer ends. Do your battle and try to catch your legend. If your going for shiny one, and it is not shiny, just throw Master Ball to save some time. Check your nature and what your IVs are (no need for exact ones) and input them to RNG Reporter. You should find what you may have hit, and IV Ranges should make it sure. If you do not find anything, make your search wider. When you find what you hit, enter it to EonTimers frame hit and Update. Your lag probaply goes up a lot. It's normal. Now just repeat and try to be really consistent.
Wild captures for E/R/S (Method 2/H-2)
Wild captures for Emerald. They are one of the easier 3rd Gen RNGs. With being able to synchronize with Method H-2, it has big margin for errors. With little luck you may hit your frame and get right encounter slot in your first try. In R/S, you don't have the change to use Synchronize, but with ID/SID abuse, you can get good shiny pokes from R/S. It is just little bit harder. Only pokemons that are required to capture instead of breeding, are Shedinja outside Poke Ball and Dittos. You might want to capture few dittos for your future breeding projects and other.
Firstly open up RNG Reporter, and select Method H-2. Search your spread with seed 0 on Emerald, and 5A0 in R/S. Remember, you can't use synchronize in R/S. Remember to have right Encounter Slot for Emerald, Ruby and Sapphire. There aren't many good spreads in low frame, but in Emerald with synchronize you can get some spreads there weren't before to appear. When you have found your spread, center +- 1 second and set IV filters to exactly your spread, and have right synchronizer. When you are looking for what frame to target, check what has right Encounter slots and try to find what has same spread nearly next to it.
Now get your catching party ready. You are going to need a catcher, synchronizer and sweet scenter. For items, just get Repels, Escape Rope and enough desired balls.
Now, you need to use Sweet Scent to get pokemon fight you. Sweet Scent takes several seconds to do, so you need to find what frame you are hitting to calibrate lag for your sweet scent. Just go to some place without synchronizer, reset your game and aim for let's say, frame 5000 with EonTimer. Press A at Sweet Scent Screen when second timer ends. Check what frame you did hit with Encounter slots and IVs. Put that to your Frame hit, update and in Lag section, you have your average sweet scent lag!
Now, just do it like normally and put that lag you found to lag. It's gonna change because normal lag, but you are now hitting closer on the first time.
Start EonTimer, Soft Reset when first timer ends. Use sweet scent when second timer ends. Search what frame you did hit with IVs and encounter slots, calibrate your timer and repeat. You should hit your frame soon.
Roamer RNG in Emerald
Okay, firstly, this is probaply one of most annoying things you can do in Pokemon. Other thing that can annoy you even more is, that if you are going for non-shiny and want to catch it in proper ball, it's gonna take really long time for even one try. And you can't do this in R/S, because there is roamer IV glitch. You can do shiny one in R/S, but IVs are failed. You should trade some catchers to Emerald before you beat E4, so you can try to catch it in right ball.
Few things to note:
1. IVs are set when your mom asks if it's blue or red.
2. You can't track Lati@s until you see it for first time.
3. Have some around 30 lvl with repel when you finish E4.
4. Always fly to Mauville and go east to Route 118 when you hunt for Lati@s.
5. Trade roamer from other game so you can see where it is with Pokedex!
Finding spread is simple part. Roamer's are generated like any other legend, with Method 1. You should pick good enough frame, because if you are wanting to do this, you shouldn't satisfy with some 25/x/15/25/15/28 Modest spread. Lati's don't receive anything special from 3rd gen, expect they can get more ribbons. Pick the best spread you can find, you are going to waste lots of time on this.
Just beat E4 and save upstairs. Use EonTimer like before. Just run downstairs and go through dialogue, and when your mom asks if it's Blue or Red, pick what you want. Thats when IVs are set. After that fly to Mauville and go east to Route 118 with Repel on. If you don't find it just repeat until you do. Check the IVs and nature of your roamer. Find match from RNG Reporters list and update EonTimer. Just keep doing this until you hit it.