Multitudini tamen rex gratior fuit quam patribus, longe ante alios acceptissimus militum animis.
Multitudini tamen rex gratior fuit quam patribus,
= rex populum romanum magis placet quam patros urbi,
[et id quod succedit difficile est]
…longe ante alios acceptissimus militum animis. : longe (adv) ante (prep) alios (m. acc pl) acceptissimus (masc. nom. sing.) militum (masc. gen. pl.) animis (dat aut abl pl.)
= Romulus acceptior animis militum Romanorum quam ullus alius dux.
I suspect the idiom here is animus, -i - that is ‘in the minds of the military…’
You’re almost certainly right. The basic meaning of anima is “breath” or “life force” and is used to mean “mind” or “soul” in a more philosophical or intellectual sense.
Animus has a broader range of meanings, which include “mind,” “spirit,” “emotions,” etc.