At 20 bbs down to which ever stack depth you think pure push- or-fold* should start (whether it’s 10/9/8/7/6 BBs — villain dependent, ideally):
Typically, you should try a mixture of limps and min-raises on the BTN. The earlier phases of the match should give you some clues about how villain will respond. Any of these BTN pf strategies can be appropriate against the right villain:
1) Min-raise ~70%+ of hands, fold the rest — because villain rarely 3-bet shoves, folds many of his big blinds, and/or plays fit- or-fold on the flop when you c-bet.
2) Min-raise ~40% of hands, limp a whole bunch more, and fold trash — because villain is a bit more active in raised pots, so you want your range to be stronger, and to be able to call a 3-bet shove pf more often than a 70% range can; but villain will let you limp without punishing you, and lets you take down limped pots reasonably often with a simple stab on the flop.
3) Similar to the above, but mix in some strong hands into your limping range — because villain perceives it as weak and has begun attacking limps pf pretty often.
4) Raise very few hands, because villain is very aggro spewy in raised pots due to drug use or whatever reason, and he will shove 52s when you make your first min-raise with AQo after limping the last gazillion hands 18 BBs deep.
OOP: Tighten up your flat-calling range from the BB. Playing fit- or-fold is way too expensive and unsustainable at this stage. You want to enter pots OOP armed with significant flopping power and/or an ability to handle villain when he has position post-flop.
Maybe he has some exploitable traits you’ve spotted, like only c- betting if he hits, or c-betting very often but folding non-strong hands to smallish check-raises, or three barrel spewing too often when you take a check-call line, such that hitting a pair will net you his bluffed off stack.
Also, monitor his BTN raising frequency as you get shallow, and review all of the hands that are +EV 3-bet shoves against someone who opens too often when stacks are short.
You can also mix in some small 3-bets against against semi- thinking, nit-at-heart players who aren’t very comfortable lagging it up (in this case, opening more BTNs than they’d like), and are doing so half-heartedly because they think they should as blinds go up. (That was a retardedly specific villain profile; small 3-bets when shallow can work against a number of opponent-types, especially if you balance them, but this is not my area of expertise. More of a growth area for me.)
Post-flop: Keep a very close eye on stack-to-pot ratios if you and villain start putting bets in on the flop or beyond. It is very easy to cross commitment thresholds inadvertently, and to be priced in to make correct calls with one over and a gutshot, or other weak draws/hands, as the pot grows relative to remaining stacks. In short, constantly look ahead before putting chips into the pot and adjust your future continuing/folding plans accordingly. Try to avoid taking lines that involve calling a bet (or two) on earlier streets and folding to further pressure on later ones. Such lines are sometimes inevitable, but stacking off sooner when you feel more certain of your equity becomes more correct as the stack- to-pot ratio shrinks, especially since you can still get called by worse (or draws) as pot odds become better for villain. Compare this to taking a more inducing/pot-control/way-ahead-way-behind type check-call line earlier in the match when stacks are deeper against a barreling villain.