You can dowload save states in the resources section => https://www.speedrun.com/alex_kidd_in_miracle_world_dx/resources

Save states should be on the steam folder like that => C:\Users\USERNAME\AppData\LocalLow\Merge Games\Alex Kidd in Miracle World DX\savedata\Steam

Download all save states and copy pasta the level you want on the folder, get back to the menu and press "LOAD GAME". You don't need to quit the game to change the save state.