You can tell by looking at the map wether a FATE is boss or mob fate - boss fates center symbol is an angry looking face (and duration can go up to 30 mins where regular fates go to 12 tops), while regular mob fates have a crossed axe/sword.

https://ffxiv.gamerescape.com/wiki/D...ry_Quest_Icons

The link above has a list of fate icons you can refer to, as there are more fate types than boss and mob slay.

Usually to solo slay fates chocobo is enough, I find that healer type chocobo is kinda more useful, so maybe get that to 10 and then use points on tank abilities when you get them. Watch your position so you don't pull more mobs than you can handle and you should be gtg.