i did the circle the grimers 1 by 1 when they are seperated from the group.You can do this by circling the grimers and muk which are together 1 or 2 times when they are not attacking while leaving the grimer seperated from the group uncircled. Try your best to capture the uncircled grimer before the muk and grimers break the orb. This is a goos strategy against multiple enemies i found out myself.
Anyway if you think grimers and muk was hard wait till you see salamence(i tried at least 20++ times and took at least half a day to catch it), Charizard(both times) and Entei(2nd time). The missions you mentioned can only be obtained after you complete the story after catching raikou,suicune and entei. You can access the deoxys,celebi and mew mission via ranger net(obtained after completion of story) and you have to complete the deoxys mission to obtain the celebi mission and the celebi to obtain the mew. Rayquaza, groudon and kyogre mission can be started by talking to various important chraceters after completing the story. Just to tell you rayquaza and mew are the hardest to capture out of these 6.