In the multiplayer menu press start to bring up the challenge menu, there are 4 categories and you can select 1 challenge from each at a time.
each challenge has a number of attempts written underneath, meaning if it has two and you fail once, you can try this one 1 more time before it changes.
you CAN complete the same challenges again.
the best way to do it is join a multiplayer game and keep quiting out so the challenges you have expire and that gives you a chance to find the easy ones. like kill 4 enemies, stay invisible for 90 seconds and so on.
i can confirm that if you complete a challenge and quit out it does NOT count towards the 25! There is no way as far as i know to track how many you have done in the game itself, but if you go here http://crysis3s.com/
and type your gamer tag, and look on the right side of the page it will say how many you have done.