For natural monsters, perhaps belua:
Belua immanis, crocodillus ille qui in Nilo gignitur …
That colossal monster, the crocodile born in the Nile …
Apuleius, Apologia, 8
Belua is often used for sea-monster (belua ponti) and it's sometimes ambiguous whether this means something like a whale (a natural 'monster') or something more supernatural. See for example: Ovid, Metamorphoses, 5.18; Lucan, Civil War, 8.764
Here, Lucretius speaks of the fanciful shapes clouds sometimes appear to take:
inde alios trahere atque inducere belua nimbos
after them some monster pulling and dragging other clouds
Lucretius, De Rerum Natura, 4.140 (trans. W. H. D. Rouse)
This, then, is a cross between natural and supernatural! Vergil uses it to describe a supernatural monster - belua Lernae - when Aeneas is in the underworld confronting all sorts of ghouls and horrors (Aeneid, 6.287).
Another option is portentum (from portendo). This obviously has semantic overlap with monstrum.
diram qui contudit hydram
notaque fatali portenta labore subegit,
comperit invidiam supremo fine domari
He [Hercules] who crushed the Hydra and laid low with fated toil the
monsters of story found that Envy is quelled only by death that comes
at last.
Horace, Epistles, 2.1.10-12 (trans.H. R. Fairclough)
This passage is clearly referencing supernatural monsters. It is interesting that Cicero uses both belua and portenta in the following. Perhaps he is differentiating here between both natural and supernatural monsters:
quae plurimorum saeculorum et eventorum memoriam litteris continet,
bovem quendam putari deum, quem Apim Aegyptii nominant, multaque alia
portenta apud eosdem et cuiusque generis beluas numero consecratas
deorum
[in Egypt] ... which preserves written records of the events of countless ages, a
bull, which the Egyptians call Apis, is deemed a god, and many other
monsters and animals of every sort are held sacred as divine
Cicero, De Re Publica, 3.9 (trans. Clinton W. Keyes)
Lastly, Apuleius here lists many types of scary creatures, but I think occursacula, terriculamenta, and formidamina (from formido) are all good generic terms for monsters in general:
At tibi, Aemiliane, pro isto mendacio duit deus iste superum et inferum commeator utrorumque deorum malam gratiam, semperque obvias
species mortuorum, quidquid umbrarum est usquam, quidquid lemurum,
quidquid manium, quidquid larvarum, oculis tuis oggerat, omnia noctium
occursacula, omnia bustorum formidamina, omnia sepulchrorum terriculamenta, a quibus tamen aevo et merito haud longe abes.
But as for you, Aemilianus, may that god, the intermediary between the
upper and lower worlds, repay you for that lie with the ill will of
the gods above and below; may he ever bring dead men’s forms to meet
your eyes, every shade, phantom, spectre, ghost that ever was, every
apparition of the night, every horror of the pyre, every terror of the
graveyard, to all of which your age and just deserts have brought you
near.
Apuleius, Apologia, 64 (trans. Christopher P. Jones)