After winning a run the Continue option in the main menu will be replaced by RERUN. Selecting it starts a new run using most of the previous won run's items.
Except Greed Mode, where all damage is always counted as half a heart due to its mechanics.
It may not be necessary to start a 4th lap to complete the achievement on some versions/platforms. Even if an extra lap is started, it may be quit immediately.
RERUN cannot be used multiple times in a row. After beating a RERUN, the main menu option becomes Continue again.
The run with the last character can be relaunched only via defeating The Lamb and starting Victory Lap.
After ending a Victory Lap in any way, the option in the menu is still Continue.
Starting a RERUN with Schoolbag and two active items may copy the item in the "first" slot to both slots.
Bug!
Switch Winning the run with The Soul instead of The Forgotten will start the RERUN as The Soul without any chains connecting it to The Forgotten. Switching back to The Forgotten returns everything to its normal state.