he has perfect invisibility - erases his chakra and presence.
he is assumedly the CREATOR of jinton. you know, the jutsu whos only natural enemy is a rinnegan? before you say it, ive seen zero evidence he cant use jinton while invisible.
the reason why the alliance was so afraid of him was this ability. since with it he can wipe out entire armies. in their opinion, since they had no rinnegans, only onoki could even slow mu down. of all the zombies in that army they picked mu out as their biggest threat.

lets say by some miracle you dodge jinton and detect his prescense. he has extraordinary speed, even keeping up with gaara and onoki, and dodging an ambush from kcm naruto.his sensing powers allow him to not only detect opponents from miles away, but also tell which village they are from. his flight power enables him to simply stay away from any short range taijutsu, and kenjutsu.
lets say you get past even that and land a hit. he can split his body almost instantly and put it back together.

given he has jinton we can assume he has mastery of the elements that comprise it and we know he cna use doton because thats how he flies.
for those saying its easy to find him, your wrong. you need special physical sensory powers. jiraiyas barrier is worthless vs someone with erased chakra or presence. as is any doujutsus. doujutsus allow you to see chakra and predict via sight and muscle movement. sharingan isnt predicting shit when it cant see you.

2nd mizukage fight: people forget that he had genjutsu, which affects area, not the person themselves. meaning most of the battle would have been them just trying to freaking find each other or land a hit. it could be a possibility mu came to that fight already hurt or intending to capture his rival. theres no evidence mu had any ill will towards him. like madara vs hashim it could have been a friendly rivalry gone bad. furthermore we know he faced steam tyranny, and still lived to tell onoki about it. meaning that was probably the first thing mizukage pulled out in their duels.