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From the release:
Clarification of TMNT Achievements
We understand there has been some confusion about obtaining some of the achievements in TMNT 1989 Classic Arcade, so were posting these rules in an attempt to clarify the requirements for the achievements.
TMNT 1989 Classic Arcade Achievement Rules
In order to minimize possible exploits, where a player could receive an achievement without "doing the work," the following rules were implemented:
1. A player's turtle must be alive at the beginning of the "Achievement period."
2. A player's turtle must be alive at the end of the "Achievement period."
3. A player's turtle can not have done something else during the Achievement period which would fail that achievement. Eg. Getting frozen in the freeze trap area would mean failing the achievement.
These rules were put into place since players could jump into the game at any time during the game.
In the case of Turtle Soup, the turtles need to be alive the very moment Shredder first appears in the shimmering wall of energy. They also need to be alive the very moment he is defeated.