Smeargle all i know right now will edit with more as i find them. PS some pokemon will fit the requirements but wont have all of them being attacking. Like they can learn all the types but one or two will be status moves not attacking moves. I will point them out.
Clefairy(Stealth Rocks if you count that)
And many more......
Okay look there are many of these i didnt even make it out of the kanto dex and i found so many, if you want me to add a few more i will but there are just too many to list.