Fast Yellow GF 22796 Mew

Step 1. Clear your save data with Up+Select+B

Step 2. Name yourself GF and your rival ?? (both names are important)

Step 3. Go to save your game, but reset the game shortly after the Yes/No box disappears but before any text is printed. Check your save file to see if you have over 6 (255 precisely) Pokémon in your party. If not or the save file is destroyed/does not exist, repeat steps 1-3 again until it works.

Step 4. Swap Pokémon 2 with Pokémon 10 to get 255 bag item stacks.

Step 5. Find TM30 in the inventory (from the "?" in your Rival name) and teach it to Pokémon 1

Step 6. Go exactly seven steps east from stepping outside of your house, and locate Burn Heal x0. Swap it four slots up.

Step 7. One slot above where the Burn Heal x0 is now, make the quantity read x89. You can do this by moving down on the toss menu and counting (two press down= x1, then the next down is x2, etc.) If the quantity is lower than x89, swap a different item in its place that is (x0 counts as higher or x256) and adjust to x89 (important to be different, so no swapping Master Ball stack with another Master Ball stack, etc. be careful here as swapping some items can freeze the game so save beforehand)

Step 8. We now have the Trainer ID 22796 (the same as event Mew). As your x coordinates are now corrupted, use Pokémon 1 to Teleport away (as we taught it Teleport).

Step 9. Go back to your house's PC, and store 255 "#x##" (while depositing, x255 is one slot below x0), and one TM30.

Step 10. Go to storage PC's toss menu. It should read Potion x1, "#x## x255 and TM30 x1. Press Select to move #x## x255 to the third item slot.

Step 11. Toss the TM30 x1, then toss the Potion x1 in that order. You should now have three #x## x255 stacks.

Step 12. Toss all but two of the first #x## x255 stack (its normal that you can't access all of the stacks anymore at this point)

Step 13. Attempt to swap the first stack with the second stack. One stack should disappear and the top stack now reads x1. Repeat to get one x0 stack.

Step 14. You'll notice you now have the expanded PC inventory (of 255 items).

You now need to have some very specific PC item quantities. Don't swap any stacks of the same kind, but rather just toss from them:

Item 13 quantity. x1
Item 14 quantity. x1
Item 15 quantity. x33
Item 16 quantity. x209
Item 17 quantity. x17
Item 18 quantity. x98
Item 19 quantity. x106
Item 20 quantity. x112
Item 21 quantity. x201

Step 15. Once this is complete, swap Ether x0 (item 24, from the Rival name we chose) with ASH (item 41), and then adjust the quantity of the Ether to x213.

Step 16. Close the menu. If all quantities are correct, you will now have 1 Pokémon rather than 255 and won't be able to scroll past Pokémon 1 anymore. This is needed for normality (as we will be fixing stuff back to normal and getting GF Mew); with 255 Pokémon it wouldn't add a wild Pokémon to the party and usually converts it into Magmar, Golem or MissingNo. anyway. Don't leave the room (important).

(Optional steps,

1. If you'd rather not have 152 Pokémon in the Pokédex before moving on to step 17, not only does it result in a glitch entry and rating, but the rating can corrupt box data.)

i. change the below quantities to x127, x211, x8 in that order and close PC (gives seen 152 own 151)
ii. change the below quantities to x127, x211, x27 in that order and close PC (gives seen 151 own 151)

2. If you want to fix your Rival name, go to item 23 (Rival name slot 1). Any item with an ID corresponding to a New Name character is normal. So for instance, TM30 is "?". If this TM30 is x80 it will make the name read "?" without any glitch characters, as the x80 means "(END NAME)".  https://glitchcity.info/wiki/The_Big_HEX_List )

Step 17. Adjust a few of the quantities, namely item 14 to x21 (swap in a Calcium x0 (the same as x256) below here so we can get x21 through tossing), item 16 quantity to x208, item 18 quantity to x88 and close the PC.

Step 18. If done correctly, a Level 0 Mew should appear. You only have one chance here to catch it, but you have Master Balls anyway so use one. However, be very careful not to throw from the same stack (first stack) you modified to change your Trainer ID (may be the first Master Ball stack you encounter), as this will modify your Trainer ID as well and could give you the wrong Mew!

Step 19. Catch it. As we fixed our party earlier, all that's in it should now be Mew and the "Q" glitch Pokémon. Congratulations, you now have the event Mew (although at a bad Level).

Step 20. Step outside back to Pallet Town and locate a Rare Candy stack in the expanded inventory. Use this to raise Mew to Level 5, then step back in your house. You can also train it normally. If it gains a low amount of experience, it may jump to Level 100 due to the experience underflow glitch.

Further cleaning up,

Step 21. Play the game normally up to receiving Oak's Parcel (which due to the expanded bag, will disappear). Pikachu won't appear at first, but swapping it above Q will fix this.

Step 22. Go to the Viridian City PC and change PC item 91 to x19 (it should be x22 and may be another #x##) and return to Oak's Lab. He should give you the Pokédex even though you didn't deliver Oak's Parcel. Your Rival's name won't be the same as before, this is expected. Viridian City Poké Mart can now be used, and the old man has had his coffee so you can proceed to Viridian Forest. Also you can fight your Rival normally west of Viridian City.

Step 23. If you want to release Q, first view the status of Mew and make sure it has less than 4 moves (possibly it only has Pound at this point). If you do this, you can proceed to deposit it and then release it without a game freeze.

Further notes,

If you release all glitch Pokémon and beat the game normally without seeing another glitch Pokémon, the Hall of Fame will be safe.

I think you can fix the PC items by depositing new item stacks into it (similarly to fixing the bag).

Congratulations! You now have Event Mew and a normal looking save file.

Additional note, instead of using the above method to wipe your party you can instead just depositing Qs over and over again, and if you catch a Pokémon beforehand, you won't need to deposit as much. This takes time however and you'll have to release your Qs from the box if you don't want them.