There are a number of alternative routes through Star Fox 64. To access the secret levels, follow the instructions below for each one:
Aquas: To unlock access to Aquas, you need to kill 100 enemies or more on Sector Y.
Area 6: You must complete Sector Z or Macbeth to access Area 6.
Katina: To get this one, you need to go through all seven warp rings on Meteo. It can also be reached by completing Sector Y.
Macbeth: Take out Spyborg at the end of Sector X before Slippy bites the dust. You can also access this level from either Solar or Zoness.
Sector Y: Protect Falco and fly beneath each of the archways in the lake on Corneria.
Sector Z: Go through all of the warp gates on Sector X. You can also get to it through Zoness.
Solar: Take out the entire Star Wolf crew before the bomb detonates. You can get to Solar via Katina as well.
Venom (2): This must be accessed via Area 6.
Zoness: This must be accessed via Aquas.
Once you complete the tasks outlined above, when you finish the level you are on and return to the map screen, the alternate route will open up and you are given the choice to visit the other area or not.