I forced a refresh on the icons but it'll take some time to run (probably an hour or so). Judging from some of the achievements in your screenshots, this has fixed the icons for a few of them so far.
Double-checked and it seems the API is indicating you've earned that tournament achievement.
Don't know if this is some kind of test achievement that should be hidden. Do you know if it's shown at all in the actual game? The SC2 website seems to show it on some profiles, though only the showcase is visible there, viewing a user's full list still seems to be broken (doesn't load for me at least):
https://starcraft2.com/en-us/profile/1/1/1316681
A few others like Honor the Legacy and StarCraft II Veteran are not showing up as earned in the API at all for you, weird.
They do have a legacy API for SC2 and I haven't checked that yet to see if the achievements show there. We're using the newer one which the starcraft2.com website also uses.
This is weird also:
Phase-Smith Commander icon is showing up as
https://static.starcraft2.com/starport/d0e7c831-18ab-4cd6-adc7-9d4a28f49ec7/achievements/30-62.jpg in the API but clearly shows a different one in your screenshot.
SC2 website also using that same icon for the achievement:
https://starcraft2.com/en-us/profile/1/2/126226 (check the second item in their showcase)
But yeah, assuming the recent achievement icons from the game are accurate, then it looks like the API is returning wrong names and descriptions for the achievements.