As an improved railgun that it is, does it even needs tunes?
It actually doesn't!
Only tune if you have free capa for it, when it comes to parasol, you can leave the WP tunes for later.
And this is when the parasol becomes really dumb. Beam Pump zooka would probably fit the build, but since the parasol is all types (except sup) and wasn't balanced for such use, it can net high damage scores and outclass previous air weapons that are even more cost expensive than the parasol.
Poor old weapons being outclassed by CS's stupidity.
Airs can be a lot easier to kill if you have the right carts. For example, hop instead of chasing them. It will make it so it's easier to hit them.
If you are balancing the stats for the bit and don't want to do more stat tunes, a force tune will help you to make it deal a bit more of damage.
Also, tuning ammo is dumb, even more on that bot. You will run out of bit charge ammo before or about the same time as the parasol, tuning ammo will only consume cost that could be used to make the bits and the parasol damage better.
Anyway, see if you really need to tune the parasol, and if you need to tune something on it, you will know what it is by then.
Parasol is good enough to make it so you don't really follow guidelines, you just get what you actually need.
