- 6IV legend - I highly doubt it due to fact chances are very, very, VERY low even with master badge. You can't actually IV hunt legends so you are left at RNG mercy.
I do have a really cool 3IV legend to show off tho :3
- 6IV melan - I know few people who did. Their chains were over 10k hatches however so it's also very rare. Link to one
- 6IV lab egg - this is almost impossible and I personally haven't herd of it. Best I got from labs were 3IV pokemon. Problem here is not many people pay attention to the IVs beside odds being very, very, VERY low.
- 6IV Ditto - doesn't exist and main reason why is because you can't really hunt it just like legends. Anything that you can't breed, you can't IV hunt. There is nothing to help you with increasing your odds and master badge current increase is too low that it doesn't make much difference. 5IV doesn't exist and 4IV also possibly doesn't exist. As you can see in my signature I have a high bounty for one but in the past 5 years I have yet to find a person who hatched 4IV let alone 5 or 6IV one. ;;
So far my best find is a 3IV Ditto with 168 IV sum while highest IV is 2IV ditto with 179 IV sum.
- Shiny starter - If you mean the very first pokemon you get then no. I forgot the exact reason why but I know it's impossible.
- Perfect dream mon - personally not yet but hopefully one day ;; Though I'm sure there are people who did.
- +3 shiny/albino hatch - I don't know if anyone ever hatched full party of specials (wouldn't be surprised if it happened) but 5 specials in one party did happen few times. (wrong post link, I can't find the one I wanted to post)
And to show off, I need two more 6IV genderless pokemon to complete my 6IV genderless pokemon collection. My best hatch was definitely shiny rottom while beldum was my very first 6IV genderless hatch (took over 2k eggs and ton of money...).