The main thing you should focus on when writing partner fighting scenes is the flow of your writing.
What you don't want is this: (I apologize, my examples are poorly and hastily written)
The ogre hurled himself at Jack. Holly stepped in front of Jack and thrust her spear upwards. The ogre landed on the sharp obsidian point and let out a gurgle before slumping to the frosty ground. Jack stepped away to combat a lone goblin while Holly focused her attention on the slow-moving Golem.
It sounds a bit clunky and the flow is off. You can fix this by locating where the partners are in the scene and adding more detail to avoid going from Jack did this, then Holly did this, then that... etc. (Again my writing will seem dreadful but you should be able to get the gist of the quality change from example 1 to example 2.)
The ogre hurled himself at Jack. Thinking fast, Holly quickly stepped in front of Jack and thrust her spear upwards. The ogre landed on the sharp obsidian point and let out a chilling gurgle before slumping to the frosty ground. Jack hastily thanked Holly before stepping left of Holly to combat a lone goblin. Preparing for a retaliation from the enemy, Holly moved backward to focus her attention on the slow-moving Golem coming from the foothills.
This strategy could work, or you could try POV switching. This will help exaggerate the fighting and show internal thoughts depending on what type of POV you write.
Think of your characters. How would they fight? Picture the scene - would Jack cowardly hide or would he brazenly attack? Consider how the characters would work together. Stay true to your characters - if Jack had no fighting experience, he would probably fight with his fists or blunt weapons. Also, try and have some emotion and dialogue in your fight scene. No one likes just nitty-gritty fighting without character progression. This will help make your scene as dynamic as possible.
It is a difficult thing to do because the line between too little detail on character movement and cooperation and too much detail is thin.
I sometimes scan over drawn-out battle scenes where each character's role is too exaggerated or the details are unusually long, so I would opt for only describing major details and updates on the scene. This would move the story along but still give the drama of a battle scene.
Another thing you could do would be to use staccato sentences for effect. They are dramatic and you can reflect both character's actions in quick bits. This also makes a more exciting scene.