On the first Dr. Wily stage, after the checkpoint there are two pipes which have weak respawning enemies. Use Jewel Satellite and stand on top of the pipes. It will take some time, but you will get extra lives and lots of bolts.
At the beginning of Hornet Man's stage, go right to the first ladder. Do not destroy any of the potted plant robots. Activate the shiled and stand on the second platform in between both robots. Remain standing there to destroy the missiles. Screws will automatically fall on Megaman.
If you plan on farming for screws and lives, consider going back to Plug Man’s stage after clearing it. By repeatedly playing through the stage 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 easily the most lucrative of the stages to replay for screws and lives.
Consider buying the following two specific items that will help you beyond the usual batch of extra lives and E-Tanks, especially if you're having a hard time. The first item to be considered are Shock Guards, which can be bought 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, whichwill 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 buye these two items to even the odds.