The cost of creating a new strike team is normally as follows:
40 Mission Funds for team #2
80 Mission Funds for team #3
120 Mission Funds for team #4
160 Mission Funds for team #5
200 Mission Funds for team #6
This is a whopping 600 total Funds which would take quite a while to grind for. However, with one simple trick this achievement can very quickly be done in only a grand total of 200 Funds.
Basically, never have more than 2 active teams at once. Each time you recruit a new team for 40 Funds, grind back up to 40 again, then RETIRE that team and recruit a new one. The costs downgrade based on how many you have ACTIVE, not how many you've historically ever gotten. And luckily, the achievement DOES count how many you've ever historically recruited; you never actually need 6 active at once.