The strongest evidence is that all known eukaryotes have mitochondria, which almost certainly evolved through endosymbiosis with an alpha-proteobacteria (a highly evolved group of bacteria).
en.wikipedia.org The oldest known fossil eukaryotes are about 1.7 billion years old.
en.wikipedia.org Splicing, or the removal of introns, is a major aspect of post-transcriptional modification, and takes place only in the nucleus of eukaryotes.
en.wikipedia.org As bikonts, they all descend from a heterotrophic eukaryote with two flagella.
en.wikipedia.org Sequences from aerobic, anaerobic, psychrophilic, thermophilic, halophilic, alkaliphilic, acidophilic, desiccation-resistant, autotrophic, and heterotrophic organisms were present, including a number from multicellular eukaryotes.
en.wikipedia.org