I really would like to get this as a tattoo but want to make sure the translation is correct. Thanks in advance!
A good translation for “remember to live” was given in this related question by TKR:
ne obliviscaris vivere
… although that literally means “do not forget to live.” If you want to use this – and I assume you want to incorporate the very famous memento mori – then we get:
Memento mori, quare ne obliviscaris vivere.
Literally: “Remember you must die, therefore do not forget to live.”
A repetition of memento would be quite ugly in my opinion. There would be the problem that memento mori should be read as “remember that you must die,” but memento vivere as “remember to live” (see the discussion here), which I find irritating.
The shortness of life, the inevitability of death, and the need to make good use of the time we have got, is a subject that Latin writers throughout the ages have written on. Perhaps the most famous text in this regard is the student song Gaudeamus igitur, which goes, to quote just the first stanza:
Iuvenes dum sumus.
Post iucundam iuventutem,
Post molestam senectutem
Nos habebit humus.
So let us be happy
While we are young.
After a joyful youth
And a troublesome old age
We will rest in the ground.
The first two lines are, I think, essentially a different way to look at the sentiment you want to express. But unfortunately, they strongly evoke an old-fashioned and stuffy type of academic merriment as well.
Another well-known example is Seneca's first letter to Lucilius (an English translation is available here), famous because it is short, easy to translate (although the devil is in the detail), and, well, it is the first, so lots of students get to enjoy it during their Latin education.
Here are some formulations we can steal from Seneca:
Vindica te tibi!
Literally: “liberate yourself” or “lay claim to yourself,” this means to stop time being stolen or slip away from yourself. (It means this in context, there is nothing in vindicare referring to time specifically.)
Omnes horas complectere.
English: “Seize [or: embrace] every hour.” (Seneca goes on: Sic fiet ut minus ex crastino pendeas, si hodierno manum inieceris. → That way you will depend less on tomorrow, if you grasp today with your hand.) An alternative to the terribly overused Carpe diem.