badge awarded based off of leaderboard stats?

Ah. Ok so this is a simple and hard to notice mistake. Your first badge award is included in the PlayerAdded function but the other two aren't. Replace the entire script with this and tell me if it works.

-- services
local plrServ = game:GetService("Players")
local badgeService = game:GetService("BadgeService")

-- var
local badgeId = 2100422700
local badge2Id = 2100404188
local badge3Id = 2100402260

plrServ.PlayerAdded:connect(function(plr)
    local Stats = Instance.new("Model")
    Stats.Name = "leaderstats"
    local Timer = Instance.new("IntValue")
    Timer.Name = "Time Wasted"
    Timer.Parent = Stats 
    Stats.Parent = plr

    -- add the event only for player who do not own the badge
    if not badgeService:UserHasBadge(plr.UserId, badgeId ) then
        local con -- needs to be defined first
        con =Timer.Changed:Connect(function(newVal)
            if newVal == 60 then
                 badgeService:AwardBadge(plr.UserId, badgeId)
                con:Disconnect() -- disconnect this event
            end
        end)
     end

    -- add the event only for player who do not own the badge
    if not badgeService:UserHasBadge(plr.UserId, badge2Id ) then
        local con -- needs to be defined first
        con =Timer.Changed:Connect(function(newVal)
            if newVal == 600 then
                 badgeService:AwardBadge(plr.UserId, badge2Id)
                con:Disconnect() -- disconnect this event
            end
        end)
    end 

    -- add the event only for player who do not own the badge
    if not badgeService:UserHasBadge(plr.UserId, badge3Id ) then
        local con -- needs to be defined first
        con =Timer.Changed:Connect(function(newVal)
            if newVal == 6000 then
                 badgeService:AwardBadge(plr.UserId, badge3Id)
                con:Disconnect() -- disconnect this event
            end
        end)
   end

end)

-- add time for all players
-- not this will mean they share the same clock
while true do
    wait(60)
    for _, plr in pairs(plrServ:GetPlayers()) do

       -- find stats
        local leaderStats = plr:FindFirstChild("leaderstats")
        if leaderStats then
            local timeVal = leaderStats:FindFirstChild("Time Wasted")
            if timeVal then
                timeVal.Value = timeVal.Value + 1
            end
        end
    end
end