Can a 555timer do this?
I have to agree with ahmed. The added flexibility of a uC will allow you to make changes in software rather than changing components. In addition, with a crystal you can get very precise timing.
With a 555, you will need to use 1% components to get any kind of accuracy (the errors multiply) or use multiturn trimmer potentiometers to tune the delays. either approach adds cost and complexity.
Also, if using 555s, I would set it up so you can calibrate each stage seperately.