tatta and dake have slightly different meanings.
While dake only shows "limitations", "exclusiveness" and sometimes "exceptions" as in
(Watashi) wa anata dake wo aishiteimasu
(I love only you.)
Broccoli dake wa taberaremasen
(I'd eat most anything but I just cannot eat broccoli.)
Sono teikiken wa 6kagetsu dake yuukou desu
(The pass is only valid for 6 months.)
tatta is a bit more limited in its use. As far as I k now,
on its own, it can only be used before countable nouns.
tatta 6kagetsu shika sunde inakatta
(I was only there for 6 months.)
tatta 4 jikan shika nemuremasen deshita
(I could only sleep for 4 hours.)
watashi wa tatta 2000 yen shika motte imasen
(I only have 2000 yen.)
A lot of times, however, they are used in pairs. Used together, they emphasize how "little" something is. The word "measly" comes to mind.
Watashi ga nihon ni sundeita no wa tatta 6kagetsu dake desu
(I only lived in Japan for 6 months.)
Watashi no kyuuryou ha tsuki 150000 yen desu
(I get paid 150000 yen per month.)
Eeee~?? Tatta sore dake??
(Really?? Is that ALL??)
tada, a different form of tatta is used when you are not talking about durations of time or countable objects.
watashi wa tada anata ni aitakatta dake desu
(I only wanted to see you.)
Watashi wa anata wo bujoku suru tsumori ha naku, tada tan ni shinjitsu wo itta dake desu
(I did not mean to insult you. I just simply stated the truth.)