I currently have 4 assessments on the go.
Some are due on the same day, others are a week apart. Prioritise them based on the due date.
Ideally you should be chipping away at each of them. Even if you answer 1 question per day for each assignment.
Personally I like to start on them within 1 week of receiving them, as this allows me time to draft and seek feedback from my teachers. By doing this, receiving a better mark is almost guaranteed.
That's not to say I don't work on them the night before though. The work has already been done, but I just go over the finer details.
A quick skim read, checking I've referenced in text, tick off the criteria I'm being assessed on, if it's a speech - rehearsing to ensure I'm under the time limit.
I have to stay up until midnight each night - not because of the difficulty of the work, but because my cohort are high performers, and that's how long it takes me to stay on top of all of my work, and surpass them.
You get out what you put in.