You will find Serges in the second part of Sigma's level.

When you fight him, the floors will be spiked and you will die instantly if you touch it.

Don't worry, there are 3 platforms to stand on, jump on one of them and destroy his cannons with Electric Spark.

After all 4 of the cannons are destroyed and when he is exposed, keep using X-buster shots until he dies, or if you have already unlocked Hard mode or Xtreme mode, use Rolling Shield against him until he is destroyed.

After you beat the second part of Sigma's level you will unlock the third part.

This is the final part and you have to fight all 4 bosses again
(Chill Penguin, Spark Mandrill, Storm Eagle, and Flame Stag).

Or if you have unlocked Hard mode you will face Wheel Gator, Magna Centipede, Armored Armadillo, and Morph Moth.

If you have unlocked Xtreme mode, you will face all 8 bosses.

To unlock Hard mode, you need to beat the game under Normal mode, and to unlock Xtreme mode, you need to beat the game under Hard mode.

Here are all the bosses' weapon that you earn after you defeat them:
-Chill Penguin/Shotgun Ice
-Spark Mandrill/Electric Spark
-Storm Eagle/Storm Tornado
-Flame Stag/Speed Burner
-Wheel Gator/Spin Wheel
-Magna Centipede/Magnet Mines
-Armored Armadillo/Rolling Shield
-Morph Moth/Silk Shot

I hope this helps you.