You can hide your online status on Instagram by disabling the "Activity Status" feature. To do that, go to your profile on Instagram, then tap the three horizontal lines at the top right corner to access your settings. Following that, scroll down and select "Privacy", then tap on "Activity Status". Finally, toggle off the "Show Activity Status" switch. However, by disabling this feature, you also won't be able to see the activity status of other users. Also, others will still be aware when you've viewed their messages or are currently typing a response.