After Clearing

Carry over to 2nd cycle

Can be carried over:
Status of MC (The five main parameters only)
Persona compendium (You can summon the persona even your level is lower than the persona's)
Items from maxed social links
Money (Sell unwanted items and equipment before the first round clearing.)

+ Last chance to sell items during True Ending (spoiler)

During the "true ending" dungeon, you can't go back to the real world, but you can use the TV tower to access the shops. This is your last time to sell items.

Discount items from Margaret
Number of persona in inventory will be 12 at the beginning
Play time

Cannot be carried over
Battle status of MC: LV, Max HP, Max SP
Items
Materials for equipment forging
Equipment
Analysis data of shadows
Persona from end game
Margaret's gift for finishing 50% and 100% of the social links

True ending:

+ SPOILER

1) On 3/20, talk to every social link that you have maxed.
2) When asked if you want to go home (自宅にもどろうか), choose no (いいえ).
3) Go to the elevator at Junes and choose no again when asked if you want to go home.
4) When asked if you'd like to go to the food court one more time (最後に、フードコートに立ち寄ってみようか…), choose yes (はい) and initiate an event at the food court.
5) Go to the floodplain and talk to Ryotaro
6) Go to the Velvet Room and talk to Igor to obtain the Orb of View (見晴らしの珠)
6) If you are already on the second cycle and have fulfilled certain conditions, you'll also get the Indigo Invitation Card (群青色の招待状), which will unlock the hidden boss
7) Go back to the Shopping District and talk to the gas station attendant.
8) You can now enter the hidden dungeon in the food court. *You will not be able to return outside once you do*
THIS CAN BE ACCESSED ON BOTH FIRST AND SECOND PLAY THROUGH

Death

+ SPOILER

During the second cycle, Death will randomly hide in treasure chests. You will be given the option on whether to open the chest and fight him or not - choose "yes" to engage. Upon winning, the chest will now have the ultimate equipments and weapons in the game.

World persona

+ SPOILER

After seeing the true ending, in the second play, you can fuse the World version of Izanagi (世界 伊邪那岐大神). This is a 12-persona fusion, the persona is level 91, it cannot inherit any skills from the fused personas, and it cannot be recorded in the Persona Compendium. The ingredients are:

イザナギ (Izanagi)
ザントマン (Sandman)
ナタタイシ (Nata Taishi)
ギリメカラ (Girimehkala)
ノルン (Norn)
オオクニヌシ (Okuninushi)
オルトロス (Orthrus)
カルティケーヤ (Kartikeya)
ミトラ (Mithra)
ツィツィミトル (Tzitzimitl)
クー・フーリン (Cu Chulain)
レギオン (Legion)

If you read the first character in each name from top to bottom, it says (イザナギノオオカミツクレ), which means "[make] Izanagi No Ookami". Similarly, the first one/two letters in the first nine names in English spell either "Izanagi-no-Okami" or "Izanagi-no-Okami" depending on how you put them together.

伊邪那岐大神(Izanagi Okami) （Lv.91）World
Resist: Phy, Fire, Ice, Elec, Wind
Default skills:
Megidolaon
Victory Cry
Angelic Grace
Mind Charge
Learned skills:
Agidyne (92)
Bufudyne (93)
Ziodyne (94)
Garudyne (95)
Fire Amp (96)
Ice Amp (97)
Elec Amp (98)
Wind Amp (99)

Hidden boss

+ SPOILER

On the second playthrough, you may also get an Indigo Invitation Card (群青色の招待状) from Igor if you go for the true ending route and have fulfilled certain conditions. With that, you can go to the Heaven dungeon (天上楽土) and challenge Margaret.

As of now, confirmed conditions for this event are:

• Obtained True Ending on the first playthrough
• 2nd cycle or later
• Empress social link maxed before finishing Magatsu Inaba dungeon
• The secondary bosses of all the dungeons are defeated before finishing Magatsu Inaba dungeon
• On 3/20,once you followed the True Ending path and faced Izanami,you MUST enter the Velvet Room BEFORE ENTERING TV WORLD.You will find yourself alone with Margaret and she will request a fight at the top floor of the Heaven dungeon.If you enter the Velvet Room after entering into the TV World,you wont get invitation.