If your supervisor needs to have an overall p-value per attribute rather than per level...and if you're confined to using aggregate logit analysis, then I can think of the following approach:
1. Run aggregate logit with all attributes included in the model. Write down the log-likelihood of the model.
2. Run the model again, after omitting the first attribute. (You can omit an attribute by setting its attribute coding to "excluded"). Write down the log-likelihood of the model.
3. Take the difference in log-likelihoods between steps 1 and 2 and multiply that difference by 2. That result is distributed as chi-squared. The stats test involves that chi-squared value as a critical value, with degrees of freedom equal to the number of levels in the excluded attribute minus one. The chi-squared test of course produces a p value.
4. Repeat steps 2-3 omitting each attribute one at a time from the full model. (So, if you have 5 total attributes in your study, you'll be doing this 5 separate times, where one attribute is omitted each time from the full model.)
The main flaw to this approach is if you have an attribute like brand or color for which respondents are in perfect disagreement about. For example, imagine an attribute like color with just two levels: Red and Blue. Imagine half the respondents prefer Red and the other half Blue (to an equal degree). In the aggregate, these two levels will cancel out in utility and the fit improvement in an aggregate logit model will be zero from such an attribute.