The game uses an autosave feature : it is not possible to save manually.

Autosaves occur when you return to the Bergsons' house, purchase upgrades, or adjust controls settings. You’ll notice the autosave icon in the bottom-right corner during these moments.

Since the game doesn't have mid-level checkpoints, your progress only saves when you're back at the game hub. However, you will keep all your gold and XP if you die.

If you're in the middle of a level, there's no way to save and resume from where you left off. To keep the gold and XP you've earned, you need to return to the Bergsons' house. You can do this by selecting the "Return Home" option from the pause menu. This will save your items and progress, but you'll have to restart the level from the beginning next time you play.