Cave stuff is NOT pixelart. The artist doing most of their backgrounds (Hiroyuki Tanaka) has been doing this stuff for almost 20 years now and is very good at it.
This is a bit of background from Espgaluda 2. You can see it has pretty good pixellevel detail, but is done in Photoshop and also uses phototextures in some places.

He said in an interview it takes him about 1-1.5 months to make one level like that. So if you really want that kind of quality be prepared to pay a 5 digit sum.
Let's say each bg takes 1 months of 40 hour work a week, that alone would be $20000 at $25 per hour, which is not super high. And then you would still need the sprites.
The enemies in Cave stuff is prerendered in their newer (since quite a while) games.
You do not really need that many frames for a boss at all. I mean with 3D you can easily make the boss fly in at an angle or whatever, this with pixels is quite a lot of extra work for little payoff. There are other cool ways to make bosses enter.
The player ship will use 3 frames for banking (one side can be mirrored, or slight differently shaded, so not much work to get both sides of the banking done), Then you need some animation for the thruster, death animation, some shots for the player, bomb effect if you gonna have a bomb. So a bit more than just 10 frames each, esp if each will have different shots/bombs.
Bullets should not be too hard and not take a long time. What you have to take into account is whether you gonna rotate stuff in code or have it preroated, in the latter case some cleanup should be done on the rotated stuff to not get fuzzy.
Also what about titlescreens, a HUD, score items, explosions and so on.
Realistically if you really want something on the level of Cave lookswise, you will likely need more than one artist, or one REALLY dedicated one. In either case I think a fair price to pay for all of this is around $30000, if you really want that quality.
And the time taken will be quite a while, with all the backgrounds and such. At least half a year, if not more (again, if you want Cave kinda quality)