How long did it take the Noldor to cross the Helcaraxë?

Question

The journey across the Helcaraxë was difficult and perilous, but how long did it take to reach Beleriand?

Answer 1

Around twenty years.

In the earlier version of the Annals of Aman in History of Middle-Earth V, where it is noted that each Valian Year (VY) "is as ten years of the Sun now are", we have:

VY 2998-3000: Now Fingolfin [...] won their way at last with grievous losses and with minished might into the North of Middle-earth.

So it took two Valian years, or twenty years in the usual reckoning.

Answer 2

One hundred and forty-four years

Around 1959, Tolkien wrote a series of notes working out the final chronology of the First Age. These reflect a recent change that he had made regarding the length of a Valian year. Previously, in 1951 he had done it as 5VY, which was then equivalent to about 50 years. Now he had changed each Valian Year to the equivalent of 144 sun years, and felt the dates of the journey needed to be revised.

Note in the "Tale of Years" that 5 VY is allowed for the wanderings of the Exiles, 1495 to 1500, but that was reckoned on a scale of 1 VY = 10 SY, and so was insufficient, being only 50 Sun-years. It is now far too much, being 720 years! Adequate would be 1 Valian Year = 144 [SY]. Therefore the Crossing of the Ice should be in FA 1496.
_{The Nature of Middle-earth - "Difficulties in Chronology"}

The Valian Year spent in reaching Beleriand via the ice aged all the Exiles about 2 years (it took 144 Sun-years) = 72 (but Feanor reached Beleriand in one half the time = Bel. 50 and so only aged 1 year). As soon as they reached Beleriand the rate quickened to 50 = 1.
_{The Nature of Middle-earth - "Difficulties in Chronology"}

As soon as the Exiles left Valinor their ageing and growing rate increased. Those who had to make way on foot and cross the Ice spent a Valian year(= 144 [sun-years]) on the journey after the doom of Mandos. This dreadful journey aged them all to an extent of about 2 [Valian] years (or 72: 1). As soon as they stepped on Middle-earth the growth rate leapt to 10 : 1.
_{The Nature of Middle-earth - "Ageing of Elves"}

The journey to Middle-earth [took] 144 [sun-]years but counted as 2 [life-]years ... We still have to alter the arrangement during the march from Aman in VY 1496. This occupied 144 sun-years; but it was so horrible that the mature aged at a double rate 2 [life-]years during that time.
_{The Nature of Middle-earth - "Ageing of Elves"}

Note that this all reflect Tolkien's final view on the matter. In previous, now rejected, versions of the legendarium, the crossing had taken anywhere from about six years to about seventy years.