The following is taken from http://strategywiki.org/wiki/Xevious/Walkthrough
- There are four secret flags that occur in the first 16 stages.
- They always appear along the same horizontal strip
of the stage, but their location within that strip is random
- In order to find it, you must carpet bomb the particular strip in order to expose the flag.
- Finding the flag earns you 1000 points, but touching it earns you an extra life (or 10,000 points depending on the arcade dip switch setting).
1. The first flag can be found along the leading edge of the first full length river in the first stage, as seen in the first picture below. Keep the target along the southern edge of the river or you will overshoot the flag.
2. The second flag lies along a line through the mouth of an inlet shown in the second picture. It is typically found in the right half of the screen, so start at the center and bomb to the left until you uncover it.
3. The third flag occurs in the large ocean after a mothership encounter. It lies along a line through the end of the longest pier. It can be anywhere on this line, so start bombing at one edge of the screen and continue all of the way to the other edge.
4. The fourth flag is hidden at the bottom of the tail feathers of the bird shown below. The bird shows up in the terrain during the second set of rotating walls.
As the other solutions suggest, it is easier to get the first flag by just replaying the first stage over and over. However, I thought that it would be useful to know where other flags can be found.Please either comment below or send me a Personal Message if you have any comments or improvements.