Continuing sets you back a few stages and resets your score to 0... may as well restart from the beginning in that case.
It gets really hard when there are a lot of those powerups that make you jump really fast, and almost all the platforms are tiny ice or conveyor belts or tiny moving platforms.
Here's my screenshots checking out all the small details in the hub area.
Started the campaign mode, Octo Valley.
The first world is very easy and boring. There's no challenge at all, and it's all very linear. Then I got to the first boss... That was actually kinda fun... and then the 2nd world is where the game started getting way more creative and fun with its enemies and obstacles.