You need 1127 XP to get to rank 10 with a legend and a FFA map (lasting 4 minutes) gives 188XP.
It needs to be with the same character so if you haven't bought any characters, you'll need to put aside a few hours within one week - I don't believe a private game adds to your rank (???) but any game involving matchmaking should be valid (haven't checked XP gains on other game types)
It is possible to unlock two legend trophies with one character at the same time (for instance I used Cassidy to get both the grapple hammer and blasters achievement), but I don't believe this counts double for the trophies that need multiple legends at level 10
Happy hunting!