Looking for your list of impactful Lives that began no earlier than 01 Jan 1901 but ended no later than 31 Dec 2000; i.e. completely within the span of the actual technical 20th century.
These can be for good or ill, but a lifespan completely within the 20th century is the main qualifier here.
Can be heads of state, political leaders, musicians, actors, athletes, innovators, entrepeneurs, religious figureheads, media, celebrities of other ilk.
People who had a huge impact on the 20th century but were born in the 19th century are automatically DQed for this. So, good bye Mahatma Gandhi, good riddance Adolf Hitler, so long Albert Einstein. Y'all born too soon.
Likewise, people who had a huge impact for good or ill on the 20th century but lived into the 21st century are also automatically DQ'ed. Sorry, Muhammad Ali, can't help ya Christopher Lee, bye bye Paul McCartney (also DQed by still living), can't do much Pope John Paul II.
Hmmm ... in no particular order, for good or ill, and mostly from an American POV:
A. Frank Sinatra (1915 - 1998)
B. Martin Luther King Jr. (1929 - 1968)
C. John F. Kennedy (1917 - 1963)
D. John Lennon (1940 - 1980)
E. Jackie Robinson (1919 - 1972)
F. Richard Nixon (1913 - 1994)
G. John Wayne (1907 - 1979)
H. Wilt Chamberlain (1936 - 1999)
I. Elvis Presley (1935 - 1977)
J. Malcolm X (1925 - 1965)
K. Frida Kahlo (1907 - 1954)
L. Florence Griffith Joyner (1958 - 1998)
M. Marilyn Monroe (1926 - 1962)
N. Indira Gandhi (1917 - 1984)
O. Wilma Rudolph (1940 - 1994)
P. Jesse Owens (1913 - 1980)
Q. Joe Louis (1914 - 1981)
R. Thurgood Marshall (1908 - 1993)
S. Janis Joplin (1943 - 1970)
T. Kurt Cobain (1967 - 1994)
U. Tupac Shakur (1971 - 1996)
V. Bob Ross (1942 - 1995)
W. Lyndon B. Johnson (1908 - 1973)
X. Jimi Hendrix (1942 - 1970)
Y. Bob Marley (1945 - 1981)
Z. Charles M. Schultz (1922 - 2000)
That's 26 right there.
Who else could be added to the list?