How to make badge counter?

There isn't enough code here to determine exactly what you problem is. For example, I don't know if you are instantiating the leaderstats or not.

However there is a glaring logic error that I can see. You are using elseif, which will only execute if the condition of the if statement that came before it wasn't true. You want to count EVERY badge the player owns not just the first one.

Cascading if statements is not the best way to accomplish this. It would be more efficient to loop over an array of the badge IDs.

Example:

local BadgeService = game:GetService("BadgeService")
local badges  = {229929415, 229929797, 229929912}

local function countBadges(player)
    local numBadges = 0
    for _, badge in next, badges do
        if BadgeService:UserHasBadge(player.userId, badge) then
            numBadges = numBadges + 1
        end
    end
    return numBadges
end

game.Players.PlayerAdded:connect(function(player)
    local leaderstats = Instance.new("Folder", player)
    leaderstats.Name = "leaderstats"

    local badges = Instance.new("IntValue", leaderstats)
    badges.Value = countBadges(player)
end)

EDIT

local BadgeService = game:GetService("BadgeService")
local badges  = {229929415, 229929797, 229929912}

local function countBadges(player)
    local numBadges = 0
    for _, badge in next, badges do
        if BadgeService:UserHasBadge(player.userId, badge) then
            numBadges = numBadges + 1
        end
    end
    return numBadges
end

game.Players.PlayerAdded:connect(function(player)
    local stats = player:findFirstChild("leaderstats")
    local cash = stats:findFirstChild("Badge")
    cash.Value = countBadges()
end)