The Rush Jet Adaptor is acquired differently in Mega Man 9 than fans may be accustomed. Instead of getting it when defeating a specific Robot Master and assimilating the skill along with that Robot Master's weapon, the Rush Jet Adaptor is earned by Mega Man after any five Robot Masters are slain. When the fifth is killed, Roll and Auto will automatically give Mega Man this adaptor.
Below is the suggested order to defeat the Robot Masters in, as well as which weapons to use on both them and the bosses in Dr. Wily's castle. Keep in mind that in terms of the Robot Masters, you can jump in at any point, but we recommend starting with Galaxy Man and going from there.
Boss Order / Weaknesses
Galaxy Man - Use Mega Buster
Jewel Man - Use Black Hole Bomb
Plug Man - Use Jewel Satellite
Tornado Man - Use Plug Ball
Magma Man - Use Tornado Blow
Hornet Man - Use Magma Bazooka
Splash Woman - Use Hornet Chaser
Concrete Man - Use Laser Trident
Wall Shooters - Use Mega Buster
Giant Machine - Use Laser Trident*
Blob Monster - Use Black Hole Bomb
Dr. Wily #1 - Use Mega Buster
Dr. Wily #2 - Use Mega Buster
Dr. Wily #3 - Use Plug Ball**
* - The Laser Trident is the weakness of all three sections of this boss, but the middle section is made much, much easier by using the Tornado Blow on it.
** - The Plug Ball is the primary weakness of Wily's final form (the UFO). However, if he appears too high to attack with the Plug Ball, quickly switch over to the Hornet Chaser and use it on him. They will hit him high above for only one bar of energy per strike, but it will help you decrease his energy a little bit more.
Dr. Wily stage: Easy extra lives
On the first Dr. Wily stage, after the check point there are six pipes. Two of them have weak respawning enemies. Use Jewel Satellite and stand on top of the first set of pipes. You will occasionally get extra lives and a lot of bolts. You can use this trick to replenish lives lost from the puzzle that is up the ladder. This also helps when completing challenges. Note: This requires a lot of time.
Hornet Man stage: Unlimited screws
You will need the Jewel Satellite in order to do this trick. In the beggining of Hornet Man's stage, move to the right until you reach the first ladder. Without destroying the potted plant robots, activate the shield and stand on the second platform in between both the robots. If you remain standing there, the missiles will be destroyed and the screws will automatically land on Mega Man. This also increase your kill count for your achievements.
Miniboss Weaknesses
To easily defeat the rock miniboss on Jewel Man's stage, equip the Hornet Chaser. The Hornet Chaser, when deployed, will attack and damage the rock foe even when he's on the ceiling, forcing him to come down where you can quickly finish him off.
To easily defeat the flame dragon miniboss on Magma Man's stage and in Dr. Wily's castle, consider equipping the Concrete Shot. Five shots to the face of the dragon with the Concrete Shot will quickly dispatch it. While the Black Hole Bomb will suck all of the flames off of the dragon's body, rendering it unable to attack, it won't heavily damage the dragon itself. Use the Concrete Shot instead.
Rush Jet Adapter
Defeat five Robot Masters to get the Rush Jet Adapter from Roll and Auto.
Screw/Extra Life Farming
If you want to farm for screws and the like, consider going back to Plug Man's stage after clearing it. By playing through the stage over and over again in its entirety, you can collect two extra lives, an E-Tank (the only E-Tank in any of the eight Robot Master stages) and around 45 screws per visit. It is indeed the most lucrative of the stages to head to in this regard.
An addition from Colin Moriarty: The Jewel Satellite on just about any stage will allow you to easily harvest screws and extra lives from unsuspecting enemies as well. The best place to use the Jewel Satellite is in the initial run on Concrete Man's stage. The birds, the rocks they drop, and the enemies that come out of holes in an attempt to knock you into them will give you endless amounts of screws and extra lives if enough time is spent. Run back and forth with the Jewel Satellite equipped during on the first section of Concrete Man's stage, respawning enemies and collecting ridiculous amounts of screws!
An addition from bergsandwich: There's another great technique to get as many screws as you need. With the Jewel Satellite in your inventory, head to Plug Man's stage. Head to the first pipe you find that spawns endless amounts of slow-moving floating robots. Engage the shield and sit right next to the pipe. Enemies will run into you from above, dropping whatever items they drop right on top of you, including small screws. Stand there for as long as needed to acquire the amount of screws you want.
Surviving
Mega Man 9 is hard. There are two specific items that will help you beyond the usual batch of extra lives and E-Tanks that you should consider purchasing with your screws if you're having difficulty. The first item to be considered are Shock Guards, which can be purchased from Auto and Roll and will allow you to survive any unintentional encounter with instant-kill spikes (once per purchase). The other item is called a Beat Call, and will automatically save you from any unintentional encounter with a pit or chasm (once per purchase). If you're having difficulty getting through any given stage, especially in Dr. Wily's castle, consider a visit to the store to purchase these two items to even the odds.