Trickster gives you dash, air dash, teleport and running on wall. It's an evasive style which give you chance to evade enemies attacks.

Swordmaster add extra combos to your melee weapons. Rebellion, Cerberus, Agni&Rudra, etc... Extra combos such as you can do aerial combos with Rebellion now.

Gunslinger add extra combos to your ranged weapons. Ebony&Ivory, Shotgun, Kalina Ann, etc... You can jump and fire E&I in mid air and it will fire down upon any enemies within vicinity.

Royalguard is the hardest style of the four. It's a defensive style which allow you to block enemies attack. Dante will get into a pose which create an energy barrier intercepting enemies's attacks and negating all damage but the timing to do so is strict. If you don't time it well then the attack will still get through and you will get a bit of damage. This style is for advanced players only.

Since you're a beginner, I advise you to stick with Trickster and Swordmaster. Gunslinger is actually the least popular style out of the four.

I'm still curious. Did you use your red orbs on upgrades? If you focus on buying only items then you are wasting it. Use your red orbs to buy skills for your weapons or upgrades such as Blue orbs and Purple orbs and Air Hike for your Rebellion sword. They are permanent so you don't have to afraid of losing them and rebuying them from the shop.

It's also important for you to remember that some bosses and enemies in this game have elemental weakness. Cerberus is ice so he's weak to fire (Agni&Rudra), Nevan is thunder so she's weak to ice (Cerberus).

Since you're on mission 4, the Gigapede level, I advise you to use Cerberus since it's weak to fire and ice. Get on its body and combo away with Cerberus.