It would be nice to know what program was used to create the title image. It's been pixeled very nicely but there is quite obvious HAM bleeding.
Later art applications were able to reduce these artefacts automatically.
Phantom Fighter uses dual playfield mode which leaves just 8 colors for the background.
In this level three colors are used to create a sand storm which is animated via color cycling.
This leaves just 5 colors for the rest of the background.
The levels in Phantom Fighter are stored as one large bitmap which is also the reason why they are so short.
The background enemies and other elements are only drawn while the player is able to see the area on screen.
The lava in this level is again animated via color cycling.