A great official walkthrough
Azure Striker Gunvolt is a pretty great platformer that unfortunately arrived in a crowded space. Hopefully people are still celebrating it and picking it up, but in the meantime, developer Inti Creates has provided a video showing off how to earn a coveted S+ rank in the first stage.
Basically it involves not getting hit and killing as many enemies as possible, but you may pick up a few pointers by watching the run.