The 2nd Anniversary Stamp Missions were a set of special missions available from September 30th to October 12th 2022 on the Japanese server, and available from December 7th to December 21st 2023 on the Global server.
There were 14 stamp card options, each with 7 missions, and players could choose 3 of the 14 to complete. Rewards included tickets for the (2nd Anniversary) 10 Free Gacha, crystals, wish pieces, and character rank EXP. There are 4 categories of stamp cards, each with different mission types.
Translations from pjsekai_eng with slight modifications.
There are 6 Unit category stamp cards, each with the same missions and rewards. The only difference between these missions is the unit specified in missions and character EXP rewards. 2 cards from this category could be chosen.
Mission
Rewards
Play 10 lives with only members of [unit] on your team
10
Watch a Virtual Live while wearing either "[unit] Happi Coat" or "[unit member] Support T-Shirt"
10
Play [unit]'s songs 10 times
10
Play 10 lives with a [unit] member's Another Vocal
10
Clear a Multi Live with all players equipping a "[unit member] Fan Title"
10
Get 4 [unit] member's costumes
10
Get 10 of [unit] member's cards, including duplicates
10
Complete all missions
1 3 per Character 300
Gameplay Stamp Cards[]
There are 3 Gameplay category stamp cards, with increasing degrees of difficulty and rewards. 1 card from this category could be chosen.
10
"[unit] Happi Coat" or 
"[unit member] Support T-Shirt"
"[unit member] Fan Title"
1
3 per Character
Countdown to Christmas! to level 50
"Journey Dance" avatar motion
Journey in Multi Live with 4 of your friends
500
Music Cards