Remember that weapons are a literal Arms Race, so the evolution will trend to the better killing weapon. The question really is what are the aliens killing most regularly.
Main Concerns would of the alien's background in deciding the transformation of the firearms (assuming your exclusively want firearms):
Change your projectile/technology to match the mechanism of lethality of your alien species.
Eg. Slug/bullet based weapons wouldn't be very effective against fast-healing, tough or organ/blood redundant beings. Eg. You may have to rely on heat, cold, poisonous or explosive weapons.
Fast agility/flight may necessitate the use of scatter weapons (shotguns) for accuracy.
Body Shape - How they hold the weapon or "Pull the trigger" so to speak
Number of Hands - Human firearms are built with 2 hands in mind.
High Gravity environments might necessitate laser/beam/high-velocity weapons
Underwater combat necessitates the use of heavy darts/harpoons as a
Natural Occurring Resources: Eg If Depleted uranium and C4 was naturally
occurring. So they can develop Armor Penetrating, they'll have access to some pretty energy dense firearms
Overall you should analyse the transformation of gunpowder/firearms in history and introduce your own divergence.
A tentative firearm advancement timeline appears as follows:
- Rocket Stick
- Musket - Matchlock/Percussion Cap
- Smoothbore vs Rifled Barrels
- Repeating Action
- Special Ammunition
The formula for gunpowder has similiarly evolved a lot of the centuries.
- Niter Saltpeter
- Black Powder
Overall general metrics for specific details of firearms come down to trigger mechanism, ammunition cycling mechanism, rifling turn rate, bullet velocity, weapon weight/ergonomics/length, ammunition calibre, ammunition capacity, ease of manufacture and material.
If we remove the gunpowder restriction, it's all about the physics of concentrating chemical/kinetic energy into a kill weapon at range.
Perhaps the aliens can generate bio-electricity for electric based weapons (a primitive coil gun perhaps) or vents gas it can detonate in the place of gunpowder.
Perhaps this alien can create a bubble of plasma/launch projectiles from the ultra fast snap of it's claws - Cough Super Alien Peacock Mantis please.