Stupidly, I had deleted my saved game last time I played this. So I had to start again. Luckily, it didn’t take long to get to the point I was at previously (the end of first world boss).
Defeated him, and worked my way through all of World 2. Bought a few power-ups on the way, including the floaty-umbrella one, and some more energy and “emotion bar”. I’ve also done the first level of World 3 too.