Watch Me Make a Boss Battle Theme in 60 Seconds

A fast tempo is the main ingredient: the sense of acceleration felt by the player will create excitement, which will be heightened even further when they see the boss.

I use a taiko drum to give the music a warlike character, with a "3 + 3 + 2" accent pattern that gives the rhythm forward momentum.

This creates what is called a "syncopated" rhythm: strong beats become weak, and vice versa.
This alternation between strong and weak captures the feel of combat.

I also add a restless snare roll. A short repetition at the end of the block gives an extra push into the next section.

Next, I use a piano, alternating a low note with the same note one octave higher, and repeat this pattern on different notes. It's that small step from C to C-sharp that makes the riff sound uneasy.

For the synth, I use high notes and short scales going down. That contrast with the busy rhythm underneath is unnerving.
The notes I'm looking for have an unstable sound, one that suggests danger.

To complete the arrangement, I bring in brass or woodwinds for an orchestral sound. I add offbeat notes to make the syncopation stand out even more.

With that fast pace, those tense melodies and the syncopated rhythm, you can tell straight away that it's a boss battle track.