Corrections to the original Blaster Master post:

1) There is no level 9. (The final level in the game is level 8, unless there is a bonus / secret level not mentioned on GameFAQs.)

2) No, you can't face the bosses in any particular order. This is because the entrance to each new level is guarded by something which you need from the last level's boss.

3) Blaster Master was still in a sense linear, only that you had to go back through old levels in order to find the entrances to new ones.

Here are list of the devices that you get from each boss:

Level 1 Boss: "Hyper" - Makes your tank's bullets larger. Allows you to defeat the wall object blocking the entrance to level 2.
Level 2 Boss: "Crusher" - Certain wall blocks can be destroyed only when you have this weapon. Incidentally, the door to level 3 is blocked by one of these. Also, a shortcut between level 1 and 3 exists when destroying these blocks.
Level 3 Boss: "Hover" - Allows your tank to fly for short periods of time. In order to get to level 4, you must go all the way back to Level 1, where you first start out, and fly upward until you reach the top of the level.
Level 4 Boss: "Key" - The least inventive of all the items. The wall blocking level 5 is guarded by a key on both sides. Open the first lock, climb out of your tank, climb the ladder, and descend downwards, and open the lock from the other end.
Level 5 Boss: "Dive" - Lets your tank hover within water. Without it, your tank is useless after descending to the bottom of level 5.
Level 6 Boss: "Wall 1" - Lets you walk up walls. The entrance to level 7 is within level 2, which means you must go from Level 6 back to 5, through 4, back to 1, then forward to level 2. You will not be able to use Hover to reach level 7. This is because the wall you must ascend is much higher than what hover will allow you to travel.
Level 7 Boss: "Wall 2" - Lets you walk on ceilings. The entrance to level 8 is in level 3, so you must go from Level 7, to 2, and then to 3.
Level 8 Boss: Game over.