I would start with two analyses: 1) correlate RT and Accuracy within each group, broken down by difficulty.  You could then look at differences in correlations for each cell between groups.  2)  I would try running two separate 2x3 ANOVAs, one for RT and one for accuracy: 2 (Group: Healthy vs. Experimental) x Difficulty (1,2,3).  Followup significant differences with post-hoc tests.  

Hello Eoin,

To answer your question thoroughly, could you please describe how RT and accuracy are measured, what units (range, etc.). 

Regards, Witold

Hello Eoin

For each outcomes, you can use factor ANOVA (between group, within group(repeated measures)).

Regards, Hesam