"I saw them with my own eyes!"
Translation:Viděl jsem je vlastníma očima!
It is a more common idiom (and it is accepted), but "vlastníma očima" is not impossible (24 hits in the corpus, some of them with a slightly different meaning) and it is closer to the topic of this skill.
I´m not saying that it is not possible to use it at all. But in this sentence, it sounds unnatural.
You cannot use the infinitive here, you need the past participle (also called the l-participle).