Wrong section first of all it should go in this section of the forum: http://www.urban-rivals.com/community/forum/?mode=viewtheme&id_theme=4
But the answer is use a card that has this ability: -X opp damage mine Y
The ability (or bonus) can't be countered by Stop Opponent Ability or Stop Oppenent Bonus and the opposing card must have more damage then the minimum.
You have a Winston in play and your opponent uses Jessie, Winston's ability won't help you towards your mission because Jessie has only 2 damage and Winston's minimum is 3.
You have a Winston and your opponent is using Kolos. Kolos's ability is + 6 damage so he has 10 damage now but Winston blocks 3 of his damage and you are dealt 7 instead of 10 and the mission will go up by 3.