The game manual provides some cryptic hints with references to classical stellar nomenclature or pop culture, and make sense only by context. If understood, the hints provide some rough suggested walkthrough.

1. In house sustenance is required for the task that awaits you.
Possibly that you must enter the first building right in the beginning of the game (Ganymede Store) in order to build up your shield and fuel.
2. In the cupboard that is bare, Jerry mouse may find a Royal reception. However,before you roll back the carpet make sure that you are well fed.
In the first room of Ganymede store there is a "mouse hole" which you can enter by crouching. Shooting the carpet ("royal reception") makes it disappear, revealing an opening to the underground tunnels. However when the carpet disappears, the fuel rod also disappears, so you must be "well fed" first.
3. Turn to the Axeman to provide an opening to the brightest star.
Shooting the axe symbol on the wall will trigger a secret opening on the Callisto Store in the Sirius Sector (Sirius = the brightest star in the earth sky).
4. The brightest speck of the Dog star is where you should start your crusade.
Normally the first sector you enter is Sirius Sector. One of the two ECD's is free so it will be a good idea to shoot it first. (Dog Star = another name for Sirius)
5. Crossing the kennel of the lesser dog, beware of getting your goose cooked by microwaves.
Probably a warning that Procyon Sector contains a radar beacon. (lesser dog = Canis Minor which contains the star Procyon)
6. Within the east end, the decrystallisation of the gem in the eye of the southern fish will allow you to head towards the land of the penguins.
Possibly a hint that the eastern ECD in Fomalhaut Sector is free and destroying it will enable you to destroy other ECD's southwards (southern fish = Pisces Australis, which contains the star Fomalhaut as its "eye").
(there is no #7 hint, perhaps on purpose)
8. Emulate the journey of Scott the Adventurer.
Possibly a reference to Robert Falcon Scott who made the journey to the Antarctic, and a hint to go southwards to the Light Side (the southern pole).
9. Head for the god of waters large heavenly body and remove the sun's influence in three areas.
Traverse the Light Side to reach Triton Sector, and destroy the three free ECD's (god of waters = Poseidon aka Neptune; Triton = a Neptunian moon).
10. If you're too left wing,you could find yourself out of your depth.
A suggestion to exit the Triton Sector to the north, and a warning to be to the right side of the screen; most of the Ganymedes Sector is water, so entering the proper way will land you safely to the next Sector.
11. You do not need any support when in the company of the cup bearer to Zeus.
A hint to destroy the pillar supporting the structure, which will fall on a Plexor, destroying it. (Ganymedes = the cup bearer to Zeus, and a satellite of Jupiter)
12. Whilst in orbit around Saturn, remember there are two sides to every argument, but one more to this clue.
Perhaps a reference to the triangular ("two sides + one more") exit from Iapetus to Sirius Sector (Iapetus = a satellite of Saturn)
13. Don't be square - Go for it!
14. Animated Mondrian provides the next step.
15. The Argonauts went in search of the Golden fleece, their vessel will ship you to new heights.
An obscure reference to the Canopus Walkway (Canopus = a prominent star in the Argo Navis constellation; Argo = the Argonauts's ship)
16. We've got the green light, who's going to use it?
Possibly a reference to finding the green teleport crystal on the walkway.
17. Defect to the east. Do not pass go. Do not collect -200.
Possibly a suggestion to leave Canopus to the east, and a warning to leave by using a jetpack to descend it (the number might refer to the in-game altitude meter)
18. The postal service is so expensive these days.
19. Head for the seedier side of the tunnel. Or as the electrician's wife said, "WIRE YOU INSULATE?"
The phrase is from an old joke. It possibly refers to the secret lamp that appears in the tunnel. Shooting the wire reveals a teleport crystal.
20. Use BR's underground to get to the middle of this place. The death of another crystal must fall on deaf ears.
A hint that Umbriel Sector is guarded by two radar beacons so you can enter it only through the tunnel hole. After destroying the radar beacons, you can then destroy the free ECD. "BR" may be a reference to British Rail (Incentive was a British company).
21. Take the cubed root of 729, multiply by 10 and add the first number you didn't think of and head in the direction. Shoot the eye of the southern fish.
${\displaystyle {\sqrt[{3}]{729}}}$ = 9 X 10 = 90. The "first number you didn't think of" is probably 7, as this number is missing from this list, perhaps on purpose; however it is not clear what is the meaning of the number 97 as a direction. In any case, it refers again to Fomalhaut Sector as the "southern fish", as you can now destroy another ECD.
22. Stride out under the heavens to reach this land.
Perhaps it means to move to the southern exit, to the Monoceros Sector (see below).
23. Blindfold the unicorn completely.
Having destroyed the previous ECD's, you can now destroy both ECD's in the Monoceros Sector (Monoceros = Unicorn)
24. Thence onwards to usurp the King and Queen of the fairies.
Destroy the ECD's in Oberon Sector and then the two free ones in Titania Sector. (Oberon and Titania = King and Queen of fairies in the Midsummer's Night Dream)
25. The antipodes hides the next link in the chain.
Possibly referring to destroying the southern ECD of Titania Sector, leading to the Antares Sector to the south?
26. Follow the chain to destroy Poseidon's satellite links.
Obscure. It might refer to either Triton or Nereid Sector (Triton and Nereid are Neptune's moons) however the ECD's of Triton Sector have been destroyed already (see hint #9) and no context suggests that it refers to Nereid Sector. Taking into account the hints above and below, it's possible that it is a mistaken reference to Antares Sector (however, Antares is a star, not a Neptunian moon).
27. Enter the successor to the liberator. "KILL THE THREE OF THEM", said ORAC.
Obscure. Possibly refers to destroying the 3 ECD's in the Antares Sector. ORAC is a reference to the British show Blake's 7.
28. Head towards the land where the shadows are strongest.
Go to the Light Side (the only Sector where the ECD's have visible shadows on the ground).
29. Destroy the two crystals that are unable to take a bearing.
Having destroyed the previous ECD's, it's now possible to destroy both ECD's of the Light Side Sector.
30. Gut the remainder of the fish to destroy Mondrian's junction.
Destroy the remainder (middle) ECD of the Fomalhaut Sector (fish). Mondrian perhaps refers to the fact that the particular ECD is decorated with animated cubes.
31. Between 21 May and 21 June, find yourself a twin to erase.
Destroy the ECD in the Pollux Sector. The date might refer to the season of Spring, and therefore the northern hemisphere where the Pollux Sector is located. (Pollux = Castor's twin brother)
32. Now for a test of personality. Who would win?
33. Shoot to the port side. Oh, no its the wrong one - beam me up, Scotty!
34. Help the post office. No not like that you dunce! Go stand in the corner.
35. Who knows where to go next?
36. More postal pranks aRe in store for the boys in blue.
37. Answer the travel agent's call in the police phonebox.
38. Take red from orange and you will find the answer in the 11th letter.
39. I thought I could sing a rainbow, but I only know the first colour.
40. For your finale, go out in a blaze of darkness.
Obscure, but obviously a reference to destroying the last ECD and finishing the game.