Use an Iterator instead and use Iterator#remove method:

for (Iterator<String> it = a.iterator(); it.hasNext(); ) {
    String str = it.next();
    if (!str.equals("foo") || !str.equals("bar")) {
        it.remove();
    }
}

From your question:

messing with for iterators is not really good practice

In fact, if you code oriented to interfaces and use List instead of ArrayList directly, using get method could become into navigating through all the collection to get the desired element (for example, if you have a List backed by a single linked list). So, the best practice here would be using iterators instead of using get.

what is the best practice to remove items from a list efficiently?

Not only for Lists, but for any Collection that supports Iterable, and assuming you don't have an index or some sort of key (like in a Map) to directly access to an element, the best way to remove an element would be using Iterator#remove.

for (Iterator<String> iter = list.listIterator(); iter.hasNext(); ) {
    String a = iter.next();
    if (...) {
        iter.remove();
    }
}

Making an additional assumption that the list is of strings. As already answered, an list.iterator() is needed. The listIterator can do a bit of navigation too.

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Update

As @AyushiJain commented, there is

list.removeIf(...);