The Xindi and Romulan wars — he is correct about their toll
Krall is referring to two bloody campaigns in Earth's pre-Federation history.
At the start of the third season of Enterprise, the Xindi, a group of five different species from a single planet in the unexplored Delphic Expanse, had used a prototype weapon to attack Earth. The attack, which occurred in March 2153, killed seven million people, including a close relative of the Enterprise's chief engineer, Trip Tucker.
This led Starfleet to send Captain Archer's Enterprise with a team of MACOs (Military Assault Command Operations officers) into the Expanse to locate the Xindi, where they spent almost a year. The Enterprise lost nearly 30 crew members / MACOs during the mission.
Krall himself was
a MACO during this time, as revealed in Beyond. (This leads to a related question.)
It was not a full-on "war", but given the casualties suffered in the initial attack, it was certainly a bloody conflict.
You can read more about the Xindi campaign here.
The fourth season of Enterprise sets the stage for the Earth-Romulan War, a lengthy conflict beginning in 2156 that ending in stalemate in 2160. Its long-term effect was the establishment of the Federation-Romulan Neutral Zone, an interstellar no-go zone for either party that was first mentioned in the Original Series episode "Balance of Terror" and whose existence persisted into the TNG era.
The exact death toll of the war has never been reported in the Star Trek canon, but given that it was four years long, it is generally assumed to have been a costly war, with deep residual resentment on both sides. For instance, as Spock reveals in "Balance of Terror":
SPOCK: Earth believes the Romulans to be warlike, cruel, treacherous, and only the Romulans know what they think of Earth. The treaty, set by sub-space radio, established this Neutral Zone, entry into which by either side, would constitute an act of war.
You can read more about the Earth-Romulan war here.