How do you award a badge with a certain amount of leaderstats?

Good job on tabbing your code and thinking about a way to solve your problem- you're almost there!

Some things I would change:

1. Use local variables.
2. Don't use deprecated methods, such as getPlayers and getService. You should use GetPlayers and GetService in future code.
3. Give variable names a real meaning, so instead of ser you could use BadgeService as a variable.
4. Don't redefine variables when they won't change from the previous iteration- i.e., you are redefining ser in every run of the loop, but the value of ser won't have changed. Instead, define this at the top of your script.
5. Your code will be running every frame, since you only used wait with no arguments. This is bad because this code doesn't need to run that often, so it's just sucking up resources and contributing to lag. A more reasonable amount of time to wait is anywhere from 1 to 5 seconds. This may not seem like a huge change, but you will be running the code far less and achieving the same experience for the player. (This is just for reference- this isn't the approach I suggest for this specific problem, for that, see #6).
6. Since ROBLOX is an event-driven platform, it will be better to check if the player has reached enough Kills using an event rather than a loop. We can use the Changed event of the Int/NumberValue you used to see when the value changes.

All together now:

local BadgeService = game:GetService("BadgeService")

local function hookPlayerKillsAchievement(player)
    local function checkPlayerKills(kills)
        if kills >= 20 then
            BadgeService:AwardBadge(player.UserId, 561649914)
        end
    end

    player:WaitForChild("leaderstats"):WaitForChild("Kills").Changed:connect(checkPlayerKills)
end

-- Iterate over any players that might already be in the game
local players = game.Players:GetPlayers()
for i = 1, #players do
    hookPlayerKillsAchievement(players[i])
end

-- Connect the event
game.Players.PlayerAdded:Connect(hookPlayerKillsAchievement)

Some important things to remember:

• This code will only work when executed in a Script, not a LocalScript
• This code will only work in online mode, not in Studio.
• The Changed event of *Value objects acts differently than in other objects- its first parameter is the new value, not the property changed as seen in other types.