Use DART ship to do this...don't hesitate to pass through some enemies (like 3 circled ships) by using your special weapon...while you are using your special weapon you also have a shield for a little time...make your way through them and don't look back...if you don't get killed until the end you will have 4 lives to finish the level...you will have the 4th one when you reach the big circles if you played well...
after passing all the enemies and start to enter the big turning circles don't try be quick...
at the first circle there are only 2 lazers...play carefully and pass through them...you can try to hit the lazers but don't need to...
at the second and third circles you MUST hit the lazers...at least most of them...because it will be a quick kill if you don't have a shield while you are passing through...
also watch out for the other enemies between the big circles...
at the end qhen you reach the core, again DON'T try to play quickly...first hit the circle's doors and let them open...when they open then you can hit the core...and also core can hit you...from time to time 3 enemies will come after you...when they appear turn back and go left...so core can't hit you like this... hit these 3 enemies and get close to the core again...while hitting the core use your special weapon if you have...so you will also be using the shield...it is not an option not to kill those 3 enemies...and also you can fully your special weapon like this...so we need them :)
after killing and blowing up the core don't be happy because there MAY be 3 more enemies behind you...take care until the text appear on the screen...than...you can start the cheer up :)
good luck ;)