You need 1127 XP to get to rank 10 with a legend and a FFA match (lasting 4 minutes) gives 188XP (whatever position you end up with)
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. So I did this with Xull but as his other weapon is a cannon - that doesn't have an trophy so only this popped.
Happy hunting!