Hard to pin point which ones in particular for the first achievements so I needed to get some help! Sources are located below with details.
More than 80 achievements are available from the start. Some of them are secret so you will have to find out by yourself how to get those.
(Unable to list them due to character limit) Achievements can be listed here: https://tibia.fandom.com/wiki/Updates/8.6
To name a few: Worm Whacker, Vanity, Shell Seeker, Allowance Collector, etc....
Also good information on the first page about achievements in 2010 implemented https://www.tibia.com/forum/?action=thread&threadid=3506217&pagenumber=1
Achievements were implemented in Tibia 8.6, June 30, 2010. It was total of 93 achievements. So it's really hard to say which one was first. However, considering the ID of achievements, first of them would be:
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