How to clean vinyl floor tile not cleaned in 25 years
If it were my floor and I had to keep it I would test a small section with straight bleach - cracks and tile.  Let bleach sit for a good 30 mins and wipe.  Wait 1-2 days.  If there is no discoloration then that is my weapon.

I would then mop the floor with extremely hot water and bleach (10% volume).  You are going to need a mop with a scrubbing brush.  At first I would just recommend hitting the floor with the hot water and bleach and letting a bit of the solution sit on the vinyl - not enough to leak elsewhere.  After 3-4 moppings you can probably start scrubbing harder.  And you will need a steel brush for the cracks.  But the basic premise is the boiling water will shock the dirt free and the bleach will start eating at the next layer.   You could do this in 2 moppings with a heavy amount of grit or 10 moppings letting the water/bleach do most of the work.

Note:  This is just what I would do personally.  Obviously using bleach has a chance to damage the tile.  I have used bleach on many many vinyl tiles without damage though - but I am not sure all manufacturers would suggest this.