This case began when Sakura asked a number of people to meet her in the rec room. Specifically, those people were Hiro, Toko, and Byakuya.
But one of them headed out a bit earlier than the others--Toko. She got there one step ahead of everyone else and looked around for a good hiding spot. And she found it. She crawled into the locker to get out of sight. Then, from inside the locker, she saw Sakura enter the room.
Next to arrive was Hiro. When he got there, he mistakenly thought Sakura was going to try to kill him, so he panicked.
Without thinking, he grabbed a nearby Monokuma Bottle and attacked Sakura with it. Thinking he killed her, he hastily began covering up his crime. He took a magazine from the table, and forged a dying message from Sakura. To that end, he wrote down a name... Toko... By writing her name, he was hoping to pin the murder on her.
But of course Toko had witnessed the whole thing. So as soon as the coast was clear... ...she jumped out of the locker and hid the magazine on the shelf with all the others. But in her rush she made one little mistake... She put the magazine back upside down.
Soon after, she watched as Sakura slowly opened her eyes... She also saw the blood dripping off Sakura's head, and fainted. This caused her personality to switch over to Genocide Jack. When she woke back up, her second personalty also saw the blood-soaked Sakura... ...and she freaked out.
And just like Hiro, she grabbed another Monokuma Bottle and attacked her. This explains why there were two wounds on Sakura's head. Assuming Sakura really was dead this time, she set about disposing of the evidence. She gathered up the broken Monokuma Bottle shards, and the queen chess piece.
And that explains how Sakura was attacked twice with the same type of weapon. But even after those two blows, she was still alive... So then, what was Sakura's actual cause of death? It was the poison that Sakura herself got from the chem lab. She turned the rec room into a true "locked room" scenario and then drank the deadly mixture. And there, she took her final breath...
Later on, the rest of us discovered that her body was in there... We had to smash the door's window to get inside. But someone already knew what had happened, knew that she had committed suicide...
And that same someone quietly snatched the bottle of poison from off the ground... ...and while nobody was looking, replaced it with an empty protein can. They did all of this specifically to place suspicion on themselves... ...in an attempt to guide the trial to a false conclusion. And the one who went to all that effort...
...was you, Hina.