I'm not sure that this is the way to claim it, but I tried to find hard proof by exporting my anime list. (Though it seems to be buggy, as I definitely rewatched some of the shows between 1st Oct. 2021 and today, but it didn't update the dates on my list.)
Claiming:
A5: Watch an anime from 00's
https://www.anime-planet.com/anime/hack-sign-intermezzo
"name": ".hack\/\/SIGN - Intermezzo",
"status": "watched",
"started": "2021-11-01 09:03:18-07",
"completed": "2021-11-01 09:03:18-07",
E5: Watch an OVA or special
I just rewatched
https://www.anime-planet.com/anime/hack-liminality around the first days of November and marked it watched for the 2x.
A2: Watch a Chinese or Korean anime
https://www.anime-planet.com/anime/the-daily-life-of-the-immortal-king
"name": "The Daily Life of the Immortal King",
"status": "watched",
"started": "2021-11-16 10:41:03-08",
"completed": "2021-11-16 13:28:10-08"
E4: Watch an anime movie
https://www.anime-planet.com/anime/over-the-sky
"name": "Over the Sky",
"status": "watched",
"started": "2021-11-01 12:16:47-07",
"completed": "2021-11-01 12:16:47-07",
E3: Watch a 20+ episode anime
I just rewatched
https://www.anime-planet.com/anime/hack-sign from 31st October and marked it watched for the 2x a few days after.
E2: Watch a 10+ episode anime
I just rewatched
https://www.anime-planet.com/anime/hack-legend-of-the-twilight in the first half of November and marked it watched for the 2x
N1: Watch a BL, GL or LGBT theme anime
I just rewatched
https://www.anime-planet.com/anime/no-money-specials on the 7th Nov. 2021 and marked it watched for the 3x
"name": "No Money Specials",
"status": "watched",
"started": "2021-11-07 10:35:45-08",
"completed": "2021-11-07 10:35:45-08"
For the .hack series I've followed this order and I definitely started it from the last days of October:
https://www.anime-planet.com/users/Kari5/lists/hack-anime-viewing-order-79844