Straight forward achievement that should come naturally as you play and hunt the 10
'Get 100 KOs as X character' achievements.
As of writing 'RocketBot Attack' (a wave based mode against AI bots) kills count towards this achievement.
EDIT: As of Sept. 2020 kills in 'RocketBot Attack'
DO count towards character specific achievements as well. Information below is outdated, but will keep it crossed for reference. Thanks to RPM Swerve for the heads up.
If you play this mode, note that only kills towards the Knockout Artist achievement, wins towards the Crater's Hero achievement and XP to level up your character are awarded while playing 'RocketBot Attack'. Kills towards character specific achievements (like 'Get 100 KOs as whatever character') DON'T count as those need to be against real players.