Sigma's third stage is full of Maverick fights (five in total), so you'll mainly be fighting familiar faces with small section breaks in between. The final boss, D-Rex, is an interesting robot that detaches and can cause some serious damage if you're not careful.
Destroy the Mega Tortoise and avoid the cannons until you reach a dungeon entrance.
Step inside to fight your old friend, Armored Armadillo. Remember, he'll start off with a rolling attack, so dodge it until he comes out of it. Once he does, shoot him with the E. Spark to destroy his armor. From that point on you should remember what to do.
Either dodge or destroy the Battools (and get the energy capsule if you have to) until you reach the next dungeon door.
Sting Chameleon will be waiting. Shoot him once with the Boomerang Cutter so he attaches his tongue to the ceiling. Shoot him once again and repeat.
Destroy the tire and miner (you can pick up the energy capsule and weapon energy with the Boomerang Cutter if you have to) and then step through the door.
End the fight with Spark Mandrill quickly by using Shotgun Ice and consistently freezeing him (remember, don't shoot him while he's frozen and shoot him when he comes out of it instead).
Descend underwater and destroy or dodge the puffer fish. Grab the energy if you have to and then go through the door.
First, use Boomerang Cutter three times to disable some of his abilities; afterwards, use the Rolling Shield and the same tactics as before to destroy Launch Octopus.
Use the Chameleon Sting's alternate fire to dodge the various enemies in the next area until you get to the dungeon door.
Now that you have Flame Mammoth's weakness, the Storm Tornado, this fight will be cake. Shoot the Storm Tornado in front of Flame Mammoth so it passes through him twice, and remember to dodge his various attacks as you did before. To make the fight easier use Boomerang Cutter to cut off his trunk.
This boss looks like a dinosaur, and is comprised of two parts: his top half and his bottom half. His bottom half is invincible, while his top half if vulnerable to weapons (preferably the Boomerang Cutter, since that's his weakness). D-Rex's top half will frequently come off and travel towards you. If you stand directly underneath it, it will immediately come down, so dodge out of the way. If D-Rex attempts to charge you, immediately dash jump through him to successfully avoid him. Sometimes he may release a fully-charged shot. There's two ways you can dodge this: you can hide in the top corner and repeatedly tap the jump button (as that's the only way you'll be able to dodge it) or you can dash towards it as it's about to be released. Just keep shooting D-Rex's top half with the Boomerang Cutter while dodging his various attacks and it should be an easy fight.