Some of Häyhä's figures are from a Finnish Army document, counted from the beginning of the war, 30 November 1939:
22 December 1939: 138 sniper kills in 22 days[21]
26 January 1940: 199 sniper kills (61 in 35 days)[22]
17 February 1940: 219 sniper kills (20 in 22 days)[7]
7 March 1940 (one day after he was wounded): total of 259 sniper kills (40 in 18 days)[7]
Häyhä never discussed it publicly, but his own private memoir, discovered in 2017, states a number. He begins by stating that "this is his sin list", and estimates the total number he shot to be around 500.

[–] [email protected] 11 points 6 hours ago* (last edited 6 hours ago)

Also keep in mind how much (or better how few) daylight there was during that time in the Finnish winter.
Additionally, these are only the numbers of those who he killed as a sniper, not counting those who he killed using his submachine gun, which is estimated to be roughly the same number on top.

For those interested into the story, the Sabaton history video is worth watching.

And also their song White Death is neat.