The other day I was playing a game and villain pushed with 7bb (i had 43bb) and i had K7o. According to the nash charts, it says I need 16.1bb to call. How tight of a shoving range does a villain need to have to shove in this situation, if there is one, to fold?

You need 43% equity to call. which is ~the top 41% of hands. Slightly more since I would heavily discount people shoving jj+

Unrealistic...

Whatever you call with should at least break even chip wise with the opposition range.
We know the amount pushed and hence the amount to call and so we can easily calculate the break even hand equity we need.
SB: pushed to 7bb
BB: needs to call 6bb to stay in a pot that finishes with a total size of 14bb

We need to put 6bb in and so to break even we need to get 6bb out of this final pot.
Hand Equity x final pot = what we get back in the long run from any pot at showdown.
so to break even we need to get 6bb back
Break Even: (Amount to call) = HE x size of final pot
or
HE needed to B.E = (Amount to call) / (size of final pot) <<< very simple and very useful equation, worth learning this well imo.
In this case we need to put in 6 and the final pot is 14
HE = 6/14 = 0.4286 = 43% (as BitchiBee stated earlier).

So we can call with any hand that has 43% equity vs the range we put villain on, if you use an equity calculator like stove you can find the hands that have 43% or more vs any range you want to put Villain on.

Here is the Nash for this (V shoves 66.2%, H calls 50.8%):

HoldemResources Nash Results

Note that the Viallin has a range of 66.2% and against this range hands like J8o have ~43%, so J8o+ is in our range. When we find all the worst hands we call with we get a full range of 50.8% for Hero.
Also note that this full Hero range has 53% equity compared to the Vaillain range. We don't include any individual hand that does worse than 43% and so our complete range vs V's range is a good bit better than 43%, actually 53% in this case.

Also as BitchiBee states if the vilalin is likely to trap with QQ+ you can take these out of V's shove range and this allows you to widen up a bit, maybe J7o could almost sneak in as a call.

edit: I should also add that this is showing the Nash ranges and you should usually adjust from these, if the player seems easy and folds often it might be best to tighten up your call range a little to allow for this or any other edge you think you have and remember plenty don't shove the Nash ranges.

thanks for the deailed explanation, it's this that im looking for. However, im pretty sure you messed up on the ICM nash calculator results because i did not have 4300 chips i had 2300.

I think you are not reading the NASH charts right, K7o is a call with 12.4bb. There are two sides to the NASH chart a SB shove and BB call chart.

BaseMetal used the 4300 chips to simulate 43BB you had and the 7BB the villain had. Actual chips is irrelevant, effective stack is governing factor on deciding to call or fold.

Your welcome and also it doesn't matter what size your stack is in this situation, only the relative stack ie, 7bb matters.
If you started with 700 and the opposition has 2300 it would give the same results.
Although the calculator is labelled an ICM one in HU icm is always exactly the same as chip ev.

I notice from your OP that you say you 'need' 16.1bb to call, I guess you realise that any less than 16.1bb and the calling range widens and K7o will get into the Nash range.
Here HoldemResources Nash Results is a 16.1bb and according to this HR calculator K9o is the bottom call hand for the BB.

Again this can be seen by calculating the needed HE.

HE needed to break even = (16.1 - 1)/(16.1 x 2) = 15.1/32.2 = 46.9%
If you look at the range given for Nash (22+,A2s+,K2s+,Q5s+,J6s+,T6s+,96s+,85s+,75s+,65s,5 4s,A2o+,K8o+,Q9o+,J9o+,T8o+,98o) then K9o has 47.2%, and K8o has 44.5%, so K9o gets in and K8o is just outside.
Perhaps the Nash calculation you originally used had ante's added or perhaps it is for stack depth after the blinds have been removed.
Finding the Nash ranges is a complicated algorithm but given these ranges showing the ev of the hands is easy.