"At least make this" vs "make this at least" - which is grammatical?

This is not a matter of grammar, but of semantics; that is, meaning.

The two sentences have slightly different meanings. Consider:

Can we at least make this predictable?
Can we make this predictable, even if we cannot do anything more?
Alternatively: Can we make this predictable, even if no one else can?
Can we make this at least predictable?
Can we make this predictable, even if we cannot make it something more than predictable?
Can we make at least this predictable?
Can we make this thing predictable, even if we cannot make anything else predictable?
*Can at least we make this predictable?
(This option may not be very natural and might only be used with contrastive emphasis)

The above are not hard and fast, and also depend a lot on context and intonation. But the point is that shifting the 'at least' does change the meaning, however slightly.

They are both grammatical. They mean slightly different things.

Can we at least make the cat predictable?

This requests that if nothing else is achieved, the cat needs to be predictable.

Can we make the cat at least predictable?

This requests that if the cat can be nothing else, it should be predictable.