This depends on what is meant by "biggest".
The largest tsunami ever recorded occurred on 9 July 1958 in Lituya
Bay, Alaska. An earthquake measuring 8.3 on the Richter scale shook
loose around 40 million cubic yards of dirt and glacier from a
mountainside at the head of the Bay, resulting in a tsunami, or
series of waves. Although the only witnesses to the event were a
couple of fishing boats, the height was able to be determined by
scientists finding the high water mark, where the water reached its
highest point on the nearby land. This massive tsunami reached a
height of 524 metres, or over half a kilometre, the equivalent of
1,720 feet or 40 feet short of a third of a mile. This is twice the
size of the Eiffel Tower.
Although the hillsides in the bay were devastated, the damage
was very localised and minimal, as Lituya Bay is very remote, there
were very few casualties. The Lituya Bay tsunami was labeled a
mega-tsunami, but its damage was relatively small because the area
is so remote. It was fortunate that the area was uninhabited, or
else the effects could have been even more devastating. As it was,
two people died when their fishing boat sank when it was hit by the
Higher tsunamis are believed to have occurred without human
witnesses, so their heights have not been recorded.
Not the largest, but the most devastating tsunami ever recorded was
the Boxing Day 2004 tsunami. The Sumatra-Andaman earthquake on 26
December 2004 resulted in an earthquake with the magnitude of 9.3
occurring on the ocean floor near the west coast of Sumatra,
perhaps the most devastating tsunami ever recorded, the height of
the wave was only about 100 feet, far from the largest. Over
230,000 people were killed. The impact of this earthquake affected
the time of the Earth's rotation time and It caused the entire
planet to vibrate as much as 1 cm (0.4 inches).