I've gotten 3:07 with the spur and 3:00:04 with the snake >_<. I don't have any screenshots, but i do have the 290.rec files(the only things i have screenshots of are of seriousface's boss rush(non-stop), where i got 6:19)
Level up your missiles on your way down the chute at the beginning and after you beat Ballos' first form(just jump and shoot at the green things flying around)
To beat Ballos' third form, you should get in front of it at the start, then shoot up. When Ballos is on the ceiling, shoot super missiles from below until you have 12-13 left(that's how many you need to beat the last form).
Also, if you are using the spur, i found a place where you can shoot through walls : Right before the room before the room with the box of missiles, if you boost towards the timer bomb and shoot a level 2 spur shot when you hug it, it will shoot both that one, and the bomb after it saving you 5 seconds.