Analysing proportional data?

#1
Hi! I'm a masters psychology student needing a little help with a dataset I'm analysing :shakehead

Dataset:
My data has a within-subjects factor of time (i.e. first session vs last session) and a between-subjects factor of group (training vs control).

One of my repeated measures DVs looks at proportional accuracy (values between [and including] 0 and 1) during the first and last training sessions.

I'm using SPSS.

Problem:
Unsurprisingly, the residuals for these accuracy distributions are extremely positive-skewed and non-normal. Arcsin transformations did nothing to resolve this. Therefore, I can't reliably use a repeated-measures ANOVA to analyse change in accuracy over time.

The question:
Is there a test I can use to investigate improvements in accuracy over time for this data? I feel like the answer is incredibly simple but I'm losing my mind over it. Alternatively, is there a better way to transform the accuracy data so that an ANOVA can be used?

I've also attached an excel version of the relevant portion of data I'm working with (in case anyone would like a visual).

Thank you in advance for your help!